diff --git a/.idea/modellierung-und-simulation-ue1.iml b/.idea/modellierung-und-simulation-ue1.iml index 3d39ba1..d4431f2 100644 --- a/.idea/modellierung-und-simulation-ue1.iml +++ b/.idea/modellierung-und-simulation-ue1.iml @@ -1,9 +1,7 @@ - - - + diff --git a/CLAUDE.md b/CLAUDE.md index bbb85de..94f4233 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -7,7 +7,7 @@ My interpretation of them is available at docs/docs.md An UML diagram is available at docs/uml.svg ## Web -The web implementation is pure JavaScript +The web implementation is TypeScript with React and Vite (in `web/`), served by nginx via Docker (`compose.yaml` in the root) ## Python The python implementation is a single-file script, which can be run on the command line or a Jupyter notebook diff --git a/README.md b/README.md index 713fb66..5e29fb1 100644 --- a/README.md +++ b/README.md @@ -1,10 +1,29 @@ # Modellierung und Simulation Übung 1 Dieses Reposiotry enthält zwei Projekte: 1) Im Ordner "python" die Python-Implementierung -2) Im Ordner "web" die JavaScript-Implementierung verfügbar und https://sim.teier.net/ue1 +2) Im Ordner "web" die TypeScript-Implementierung, verfügbar unter https://sim.teier.net/ue1 ## Python +```sh +cd python +uv run ue1.py --animation # bunt +uv run ue1.py --experiment alle # wind, schneise, trockenheit oder alle +un run ue1.py --wind 0.8 --animation # Einzellauf +``` ## Web +Entwicklung: +```sh +cd web +npm install +npm run dev +``` +Docker (nginx, http://localhost:8080): +```sh +docker compose up -d --build +``` + +Die Web-Version verwendet einen anderen Zufallsgenerator als Python: Läufe mit demselben Seed sind reproduzierbar, +stimmen aber nicht mit den Python-Läufen überein. diff --git a/compose.yaml b/compose.yaml new file mode 100644 index 0000000..f3ed526 --- /dev/null +++ b/compose.yaml @@ -0,0 +1,7 @@ +services: + web: + build: ./web + image: waldbrand-simulation + ports: + - "8080:80" + restart: unless-stopped diff --git a/docs/docs.md b/docs/docs.md index bc2c3f1..d3da68d 100644 --- a/docs/docs.md +++ b/docs/docs.md @@ -26,6 +26,7 @@ Windfaktor für Verbreitung: Entzündungswahrscheinlichkeit eine Zelle: Distanz * Brandfaktor * Windfaktor +Rand: Der gesamte Simulationsrand ist immer eine Brandschneise Code: https://git.teier.net/teier/modellierung-und-simulation-ue1.git -Link: https://sim.teier.net/ue1 \ No newline at end of file +Link: https://sim.teier.net/ue1 \ No newline at end of file diff --git a/docs/uml.svg b/docs/uml.svg index 4854ceb..11958fc 100644 --- a/docs/uml.svg +++ b/docs/uml.svg @@ -1,4 +1,4 @@ -
Für jede Zelle
Zellenzustand
ist brennend?
Für jeden Moore-Nachbarn
Nachbarzellenzustand ist Wald?
Restbrenndauer--
Restbrenndauer == 0?
Setze Zelle auf Status abgebrannt
ja
nein
ja
nein
nein
Zufallszahl 0-100 < (Distanz * Brandfaktor * (1+ Windstärke * cos(Winkel(Vektorwind, Vektorzellen)))*50

Ja
nein
Setze Zelle auf Status brennend
Zufallszahl 0-100 < Löschwahrscheinlichkeit
*100
Initialisierung:
- Zellengitter MxN mit Zufallswerten für Typ, Restbrenndauer, Brandfaktor
- Globaler Zufallswert für Löschwahrscheinlichkeit, Windstärke und Windrichtung
Gibt es eine brennende Zelle?

nein
ja
ja
 \ No newline at end of file +
Für jede Zelle im alten Zustand
Zellenzustand
ist brennend?
Für jeden Moore-Nachbarn im alten Zustand
Nachbarzellenzustand ist Wald?
Restbrenndauer--
Restbrenndauer == 0?
Setze Zelle auf Status abgebrannt im neuen Zustand
ja
nein
ja
nein
nein
Zufallszahl 0-100 < (Distanz * Brandfaktor * (1+ Windstärke * cos(Winkel(Vektorwind, Vektorzellen)))*50

Ja
nein
Setze Zelle auf Status brennend im neuen Zustand
Zufallszahl 0-100 < Löschwahrscheinlichkeit
*100
Initialisierung:
- Zellengitter MxN mit Zufallswerten für Typ, Restbrenndauer, Brandfaktor
- Globaler Zufallswert für Löschwahrscheinlichkeit, Windstärke und Windrichtung
- Eine Waldzelle wird zufällig auf brennend gesetzt
Gibt es eine brennende Zelle?

nein
ja
ja
Neuer Zustand := Kopie(alter Zustand)
Beide Schleifen zu Ende: Alter Zustand := neuer Zustand
 \ No newline at end of file diff --git a/python/pyproject.toml b/python/pyproject.toml index 2f1367d..a53aeb7 100644 --- a/python/pyproject.toml +++ b/python/pyproject.toml @@ -2,4 +2,7 @@ name = "modellierung-und-simulation-ue1" version = "0.1.0" requires-python = ">=3.9" -dependencies = [] +dependencies = [ + "matplotlib>=3.5", + "numpy>=1.22", +] diff --git a/python/ue1.py b/python/ue1.py index 8b13789..10baf12 100644 --- a/python/ue1.py +++ b/python/ue1.py @@ -1 +1,414 @@ +"""Waldbrand als zellulärer Automat (Modellierung und Simulation, UE1). +Kommandozeile: + python ue1.py --experiment alle + python ue1.py --experiment wind --laeufe 30 --seed 1 + python ue1.py --animation + +Jupyter / Colab: + %run -n ue1.py (oder: from ue1 import *) + ergebnis = simuliere(Params(wind_staerke=0.8, seed=1)) + zeige_verlauf(ergebnis) + experiment_wind() + +Modellregeln (Kurzfassung): +- Zustände: Wald, brennend, abgebrannt, gelöscht, Brandschneise. + Nur Wald kann sich entzünden; abgebrannt, gelöscht und Brandschneise verhalten sich gleich. +- Nachbarschaft: Moore (8 Zellen), Distanzgewicht 1 (direkt) bzw. 0.7 (diagonal). +- Rand: die äußerste Zeile bzw. Spalte auf jeder Seite ist Brandschneise, das Feuer kann das Gebiet + also nicht verlassen. Jede innere Zelle hat damit iåmmer 8 Nachbarn. +- Brandherd: eine zufällige Waldzelle (durch den Seed festgelegt) oder eine vorgegebene Zelle. +- Synchrones Update: alle Regeln lesen den Zustand zum Zeitpunkt t und schreiben t+1. +- Pro Zeitschritt, für jede brennende Zelle: + 1. Mit Löschwahrscheinlichkeit wird sie gelöscht (und breitet sich nicht mehr aus). + 2. Sonst versucht sie jeden Nachbarn, der Wald ist, zu entzünden (unabhängige Versuche): + p = 0.5 * Distanzgewicht * Brandfaktor(Nachbar) * Windfaktor + Windfaktor = 1 + Windstärke * cos(Winkel(Windvektor, Vektor brennende Zelle -> Nachbar)) + 3. Danach Restbrenndauer - 1; bei 0 wird sie abgebrannt. + Eine Zelle mit Restbrenndauer d breitet sich also in d Zeitschritten aus. +- Windvektor (x, y): x zeigt nach rechts (Osten), y nach oben (Norden), + der Vektor gibt die Richtung an, in die der Wind weht. +""" + +import argparse +import math +from dataclasses import dataclass, field, replace +from typing import Dict, List, Optional, Sequence, Tuple + +import matplotlib.pyplot as plt +import numpy as np +from matplotlib.animation import FuncAnimation +from matplotlib.colors import ListedColormap +from matplotlib.patches import Patch + +# Zustände +WALD = 0 +BRENNEND = 1 +ABGEBRANNT = 2 +GELOESCHT = 3 +SCHNEISE = 4 + +ZUSTAND_NAMEN = ["Wald", "brennend", "abgebrannt", "gelöscht", "Brandschneise"] +ZUSTAND_FARBEN = ["#008300", "#e34948", "#3a3a38", "#86b6ef", "#d9d4c7"] +ZUSTAND_CMAP = ListedColormap(ZUSTAND_FARBEN) + +# Farben für Varianten in Vergleichsplots (feste Reihenfolge) +VARIANTEN_FARBEN = ["#2a78d6", "#eb6834", "#1baf7a"] + +# Moore-Nachbarschaft: (Zeilenversatz, Spaltenversatz, Distanzgewicht) +NACHBARN = [ + (-1, -1, 0.7), (-1, 0, 1.0), (-1, 1, 0.7), + (0, -1, 1.0), (0, 1, 1.0), + (1, -1, 0.7), (1, 0, 1.0), (1, 1, 0.7), +] + + +@dataclass +class Params: + breite: int = 100 + hoehe: int = 100 + # Anteil natürlicher Brandschneisen (z.B. Wasser, Fels), zufällig verteilt + schneise_anteil: float = 0.05 + # Künstliche Brandschneisen als volle Zeilen bzw. Spalten + schneisen_zeilen: Sequence[int] = () + schneisen_spalten: Sequence[int] = () + # Brandfaktor ("Trockenheit") je Waldzelle, gleichverteilt + brandfaktor_min: float = 0.1 + brandfaktor_max: float = 1.0 + # Restbrenndauer je Waldzelle, ganzzahlig gleichverteilt (inklusive Grenzen) + brenndauer_min: int = 2 + brenndauer_max: int = 5 + wind_richtung: Tuple[float, float] = (1.0, 0.0) + wind_staerke: float = 0.0 + loesch_wahrscheinlichkeit: float = 0.05 + # Startzelle (Zeile, Spalte), None = zufällige Waldzelle + start: Optional[Tuple[int, int]] = None + max_schritte: int = 1000 + seed: Optional[int] = None + + +@dataclass +class Ergebnis: + params: Params + verlauf: List[np.ndarray] # Zustandsgitter je Zeitschritt, verlauf[0] = Anfangszustand + anzahl: np.ndarray # Form (Schritte + 1, 5): Anzahl Zellen je Zustand und Zeitschritt + wald_anfang: int = field(init=False) + + def __post_init__(self): + self.wald_anfang = int(self.anzahl[0, WALD] + self.anzahl[0, BRENNEND]) + + @property + def dauer(self) -> int: + return len(self.verlauf) - 1 + + @property + def betroffen(self) -> int: + """Zellen, die irgendwann gebrannt haben.""" + letzte = self.anzahl[-1] + return int(letzte[BRENNEND] + letzte[ABGEBRANNT] + letzte[GELOESCHT]) + + @property + def betroffen_anteil(self) -> float: + """Anteil der anfänglichen Waldfläche, die gebrannt hat.""" + return self.betroffen / self.wald_anfang + + +def windfaktor(dr: int, dc: int, richtung: Tuple[float, float], staerke: float) -> float: + """1 + Windstärke * cos(Winkel zwischen Windvektor und Vektor zur Nachbarzelle).""" + wx, wy = richtung + norm_wind = math.hypot(wx, wy) + if staerke == 0 or norm_wind == 0: + return 1.0 + # Zeilenindex wächst nach unten, y zeigt nach oben + nx, ny = dc, -dr + cos_winkel = (wx * nx + wy * ny) / (norm_wind * math.hypot(nx, ny)) + return 1 + staerke * cos_winkel + + +def verschiebe(a: np.ndarray, dr: int, dc: int) -> np.ndarray: + """Liefert b mit b[r, c] = a[r - dr, c - dc]; außerhalb des Gitters 0 (kein Umlauf wie bei np.roll).""" + b = np.zeros_like(a) + h, w = a.shape + b[max(dr, 0):h + min(dr, 0), max(dc, 0):w + min(dc, 0)] = \ + a[max(-dr, 0):h + min(-dr, 0), max(-dc, 0):w + min(-dc, 0)] + return b + + +def init_gitter(params: Params, rng: np.random.Generator): + """Erzeugt Zustand, Brandfaktor und Restbrenndauer und entzündet die Startzelle.""" + form = (params.hoehe, params.breite) + zustand = np.where(rng.random(form) < params.schneise_anteil, SCHNEISE, WALD).astype(np.int8) + if params.start is not None: + # Am vorgegebenen Brandherd wächst immer Wald, auch wenn dort zufällig eine natürliche Schneise läge + zustand[params.start] = WALD + for zeile in params.schneisen_zeilen: + zustand[zeile, :] = SCHNEISE + for spalte in params.schneisen_spalten: + zustand[:, spalte] = SCHNEISE + # Rand: die äußerste Zeile bzw. Spalte auf jeder Seite ist Brandschneise + zustand[[0, -1], :] = SCHNEISE + zustand[:, [0, -1]] = SCHNEISE + + if params.start is None: + # Zufällige Waldzelle; hängt nur vom Seed und den Zelltypen ab, daher bei gleichem Seed + # in allen Varianten dieselbe, solange diese die Zelltypen nicht verändern + waldzellen = np.argwhere(zustand == WALD) + start = tuple(waldzellen[rng.integers(len(waldzellen))]) + else: + start = params.start + if zustand[start] != WALD: + raise ValueError(f"Startzelle {start} liegt auf einer künstlichen Brandschneise oder am Rand") + + brandfaktor = rng.uniform(params.brandfaktor_min, params.brandfaktor_max, form) + restbrenndauer = rng.integers(params.brenndauer_min, params.brenndauer_max + 1, form) + brandfaktor[zustand == SCHNEISE] = 0 + restbrenndauer[zustand == SCHNEISE] = 0 + + zustand[start] = BRENNEND + return zustand, brandfaktor, restbrenndauer + + +def schritt(zustand, brandfaktor, restbrenndauer, params: Params, rng: np.random.Generator): + """Ein synchroner Zeitschritt; die Eingabe-Arrays werden nicht verändert.""" + brennend = zustand == BRENNEND + wald = zustand == WALD + + geloescht = brennend & (rng.random(zustand.shape) < params.loesch_wahrscheinlichkeit) + ausbreitend = brennend & ~geloescht + + entzuendet = np.zeros_like(wald) + for dr, dc, gewicht in NACHBARN: + # Zielzelle (r, c) hat eine ausbreitende Nachbarzelle bei (r - dr, c - dc) + quelle = verschiebe(ausbreitend, dr, dc) + p = 0.5 * gewicht * brandfaktor * windfaktor(dr, dc, params.wind_richtung, params.wind_staerke) + entzuendet |= wald & quelle & (rng.random(zustand.shape) < p) + + neu_zustand = zustand.copy() + neu_brandfaktor = brandfaktor.copy() + neu_restbrenndauer = restbrenndauer.copy() + + neu_restbrenndauer[ausbreitend] -= 1 + ausgebrannt = ausbreitend & (neu_restbrenndauer == 0) + neu_zustand[ausgebrannt] = ABGEBRANNT + + neu_zustand[geloescht] = GELOESCHT + neu_restbrenndauer[geloescht] = 0 + + neu_brandfaktor[ausgebrannt | geloescht] = 0 + neu_zustand[entzuendet] = BRENNEND + return neu_zustand, neu_brandfaktor, neu_restbrenndauer + + +def zaehle(zustand: np.ndarray) -> np.ndarray: + return np.bincount(zustand.ravel(), minlength=len(ZUSTAND_NAMEN)) + + +def simuliere(params: Params) -> Ergebnis: + """Simuliert, bis keine Zelle mehr brennt oder max_schritte erreicht ist.""" + rng = np.random.default_rng(params.seed) + zustand, brandfaktor, restbrenndauer = init_gitter(params, rng) + verlauf = [zustand] + anzahl = [zaehle(zustand)] + while anzahl[-1][BRENNEND] > 0 and len(verlauf) <= params.max_schritte: + zustand, brandfaktor, restbrenndauer = schritt(zustand, brandfaktor, restbrenndauer, params, rng) + verlauf.append(zustand) + anzahl.append(zaehle(zustand)) + return Ergebnis(params, verlauf, np.array(anzahl)) + + +# --------------------------------------------------------------------------- +# Visualisierung +# --------------------------------------------------------------------------- + +def zeige_gitter(zustand: np.ndarray, ax=None, titel: str = ""): + if ax is None: + _, ax = plt.subplots(figsize=(5, 5)) + ax.imshow(zustand, cmap=ZUSTAND_CMAP, vmin=0, vmax=len(ZUSTAND_NAMEN) - 1, interpolation="nearest") + ax.set_title(titel, fontsize=10) + ax.set_xticks([]) + ax.set_yticks([]) + return ax + + +def zustand_legende(fig): + griffe = [Patch(color=farbe, label=name) for name, farbe in zip(ZUSTAND_NAMEN, ZUSTAND_FARBEN)] + fig.legend(handles=griffe, loc="lower center", ncol=len(griffe), frameon=False, fontsize=9) + + +def zeichne_kurven(ax, ergebnis: Ergebnis, farbe: str, name: Optional[str] = None): + """Betroffene Fläche über die Zeit; ohne Name zusätzlich die brennenden Zellen (gestrichelt).""" + a = ergebnis.anzahl + betroffen = (a[:, BRENNEND] + a[:, ABGEBRANNT] + a[:, GELOESCHT]) / ergebnis.wald_anfang * 100 + ax.plot(betroffen, color=farbe, linewidth=2, label=name or "betroffen gesamt") + if name is None: + brennend = a[:, BRENNEND] / ergebnis.wald_anfang * 100 + ax.plot(brennend, color=farbe, linewidth=2, linestyle="--", label="brennend") + + +def kurven_achse(ax): + ax.set_xlabel("Zeitschritt") + ax.set_ylabel("% der Waldfläche") + ax.set_ylim(0, 100) + ax.grid(alpha=0.3) + ax.spines[["top", "right"]].set_visible(False) + ax.legend(frameon=False, fontsize=9) + + +def zeige_verlauf(ergebnis: Ergebnis, anzahl_bilder: int = 5): + """Momentaufnahmen des Gitters und Zeitverlauf eines einzelnen Laufs.""" + zeitpunkte = np.linspace(0, ergebnis.dauer, anzahl_bilder).astype(int) + fig = plt.figure(figsize=(3 * anzahl_bilder, 6.5)) + raster = fig.add_gridspec(2, anzahl_bilder, height_ratios=[1, 0.8]) + for i, t in enumerate(zeitpunkte): + zeige_gitter(ergebnis.verlauf[t], fig.add_subplot(raster[0, i]), f"t = {t}") + ax = fig.add_subplot(raster[1, :]) + zeichne_kurven(ax, ergebnis, VARIANTEN_FARBEN[0]) + kurven_achse(ax) + fig.suptitle(f"Betroffen: {ergebnis.betroffen_anteil:.0%} der Waldfläche, Dauer: {ergebnis.dauer} Schritte") + zustand_legende(fig) + fig.tight_layout(rect=(0, 0.05, 1, 1)) + return fig + + +def zeige_vergleich(ergebnisse: Dict[str, Ergebnis]): + """Endzustand jeder Variante nebeneinander plus gemeinsamer Zeitverlauf.""" + n = len(ergebnisse) + fig = plt.figure(figsize=(4 * n + 5, 4.8)) + raster = fig.add_gridspec(1, n + 1, width_ratios=[1] * n + [1.4]) + ax_kurven = fig.add_subplot(raster[0, n]) + for i, (name, ergebnis) in enumerate(ergebnisse.items()): + titel = f"{name}\nbetroffen {ergebnis.betroffen_anteil:.0%}, {ergebnis.dauer} Schritte" + zeige_gitter(ergebnis.verlauf[-1], fig.add_subplot(raster[0, i]), titel) + zeichne_kurven(ax_kurven, ergebnis, VARIANTEN_FARBEN[i % len(VARIANTEN_FARBEN)], name) + kurven_achse(ax_kurven) + zustand_legende(fig) + fig.tight_layout(rect=(0, 0.07, 1, 1)) + return fig + + +def animiere(ergebnis: Ergebnis, intervall_ms: int = 80): + """Animation eines Laufs. In Jupyter: from IPython.display import HTML; HTML(anim.to_jshtml())""" + fig, ax = plt.subplots(figsize=(6, 6.4)) + bild = ax.imshow(ergebnis.verlauf[0], cmap=ZUSTAND_CMAP, vmin=0, vmax=len(ZUSTAND_NAMEN) - 1, + interpolation="nearest") + ax.set_xticks([]) + ax.set_yticks([]) + zustand_legende(fig) + + def update(t): + bild.set_data(ergebnis.verlauf[t]) + ax.set_title(f"t = {t}") + return (bild,) + + anim = FuncAnimation(fig, update, frames=len(ergebnis.verlauf), interval=intervall_ms) + return anim + + +# --------------------------------------------------------------------------- +# Experimente +# --------------------------------------------------------------------------- + +def vergleiche(varianten: Dict[str, Params], laeufe: int = 20, seed: int = 0, zeigen: bool = True): + """Simuliert jede Variante mit denselben Seeds und gibt Mittelwerte aus. + + Gleiche Seeds bedeuten: alle Varianten starten mit demselben Wald und Brandherd (gleiche Brandfaktoren, + Brenndauern und natürlichen Schneisen), soweit die Variante die Initialisierung nicht selbst ändert. + """ + statistik = {} + beispiele = {} + for name, params in varianten.items(): + ergebnisse = [simuliere(replace(params, seed=seed + i)) for i in range(laeufe)] + anteile = np.array([e.betroffen_anteil for e in ergebnisse]) + dauern = np.array([e.dauer for e in ergebnisse]) + statistik[name] = { + "betroffen_mittel": anteile.mean(), + "betroffen_std": anteile.std(), + "dauer_mittel": dauern.mean(), + "dauer_std": dauern.std(), + "grossbrand_anteil": (anteile > 0.5).mean(), + } + # Beispiel für die Grafik: der Lauf mit dem Median der betroffenen Fläche + beispiele[name] = ergebnisse[int(np.argsort(anteile)[len(anteile) // 2])] + + print(f"{'Variante':<28}{'betroffen (Mittel ± Std)':>26}{'Dauer (Mittel ± Std)':>24}{'Läufe > 50 %':>14}") + for name, s in statistik.items(): + print(f"{name:<28}{s['betroffen_mittel']:>17.1%} ± {s['betroffen_std']:>5.1%}" + f"{s['dauer_mittel']:>16.1f} ± {s['dauer_std']:>5.1f}{s['grossbrand_anteil']:>14.0%}") + print() + + if zeigen: + zeige_vergleich(beispiele) + return statistik, beispiele + + +def experiment_wind(laeufe: int = 20, seed: int = 0, zeigen: bool = True): + print("Experiment Wind: Windstärke 0 vs. 0.8 (Wind nach Osten)") + basis = Params() + return vergleiche({ + "ohne Wind": basis, + "Wind 0.8 nach Osten": replace(basis, wind_richtung=(1, 0), wind_staerke=0.8), + }, laeufe, seed, zeigen) + + +def experiment_schneise(laeufe: int = 20, seed: int = 0, zeigen: bool = True): + print("Experiment Brandschneise: Wind nach Osten, ohne vs. mit Schneise östlich des Brandherds") + # Fester Brandherd westlich der Schneise, damit der Vergleich nicht vom zufälligen Startpunkt abhängt + basis = Params(wind_richtung=(1, 0), wind_staerke=0.8, start=(50, 50)) + # Eine durchgehende gerade Schneise ist in der Moore-Nachbarschaft schon mit 1 Zelle Breite + # unüberwindbar, die Breite spielt in diesem Modell also keine Rolle + return vergleiche({ + "ohne Schneise": basis, + "Schneise in Spalte 65": replace(basis, schneisen_spalten=(65,)), + }, laeufe, seed, zeigen) + + +def experiment_trockenheit(laeufe: int = 20, seed: int = 0, zeigen: bool = True): + print("Experiment Trockenheit: Brandfaktor feucht (0.1-0.5) vs. normal (0.1-1.0) vs. trocken (0.5-1.0)") + basis = Params() + return vergleiche({ + "feucht (0.1-0.5)": replace(basis, brandfaktor_min=0.1, brandfaktor_max=0.5), + "normal (0.1-1.0)": basis, + "trocken (0.5-1.0)": replace(basis, brandfaktor_min=0.5, brandfaktor_max=1.0), + }, laeufe, seed, zeigen) + + +EXPERIMENTE = { + "wind": experiment_wind, + "schneise": experiment_schneise, + "trockenheit": experiment_trockenheit, +} + + +def main(): + parser = argparse.ArgumentParser(description="Waldbrand als zellulärer Automat") + parser.add_argument("--experiment", choices=[*EXPERIMENTE, "alle"], + help="Experiment ausführen (ohne Angabe: einzelner Lauf mit Standardparametern)") + parser.add_argument("--laeufe", type=int, default=20, help="Läufe je Variante") + parser.add_argument("--seed", type=int, default=0) + parser.add_argument("--wind", type=float, default=0.0, help="Windstärke für den Einzellauf") + parser.add_argument("--animation", action="store_true", help="Einzellauf animieren") + parser.add_argument("--speichern", metavar="PRAEFIX", help="Grafiken als PRAEFIX_.png speichern statt anzeigen") + args = parser.parse_args() + + anim = None + if args.experiment: + namen = list(EXPERIMENTE) if args.experiment == "alle" else [args.experiment] + for name in namen: + EXPERIMENTE[name](args.laeufe, args.seed) + else: + ergebnis = simuliere(Params(wind_staerke=args.wind, seed=args.seed)) + if args.animation: + anim = animiere(ergebnis) # Referenz halten, sonst stoppt die Animation + else: + zeige_verlauf(ergebnis) + + if args.speichern: + for i in plt.get_fignums(): + plt.figure(i).savefig(f"{args.speichern}_{i}.png", dpi=150) + else: + plt.show() + return anim + + +if __name__ == "__main__": 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"optional": true + }, + "jiti": { + "optional": true + }, + "less": { + "optional": true + }, + "sass": { + "optional": true + }, + "sass-embedded": { + "optional": true + }, + "stylus": { + "optional": true + }, + "sugarss": { + "optional": true + }, + "terser": { + "optional": true + }, + "tsx": { + "optional": true + }, + "yaml": { + "optional": true + } + } + } + } +} diff --git a/web/package.json b/web/package.json new file mode 100644 index 0000000..dea716c --- /dev/null +++ b/web/package.json @@ -0,0 +1,23 @@ +{ + "name": "waldbrand-simulation", + "private": true, + "version": "0.1.0", + "type": "module", + "scripts": { + "dev": "vite", + "build": "tsc && vite build", + "preview": "vite preview" + }, + "dependencies": { + "react": "^19.3.1", + "react-dom": "^19.3.1", + "recharts": "^3.10.1" + }, + "devDependencies": { + "@types/react": "^19.3.0", + "@types/react-dom": "^19.3.0", + "@vitejs/plugin-react": "^6.1.2", + "typescript": "^7.0.2", + "vite": "^8.3.5" + } +} diff --git a/web/src/App.tsx b/web/src/App.tsx new file mode 100644 index 0000000..4c71b3a --- /dev/null +++ b/web/src/App.tsx @@ -0,0 +1,45 @@ +import { useState } from "react"; +import Experimente from "./komponenten/Experimente"; +import Simulation from "./komponenten/Simulation"; + +type Ansicht = "simulation" | "experimente"; + +export default function App() { + const [ansicht, setAnsicht] = useState("simulation"); + + return ( + <> +
+
+

Waldbrand-Simulation

+

Zellulärer Automat – Modellierung und Simulation, Übung 1

+
+ +
+ {/* Beide Ansichten bleiben eingehängt, damit ein laufender Brand beim Wechsel erhalten bleibt */} +
+ +
+
+ +
+ + ); +} diff --git a/web/src/experimente.ts b/web/src/experimente.ts new file mode 100644 index 0000000..1fcb54f --- /dev/null +++ b/web/src/experimente.ts @@ -0,0 +1,94 @@ +import { simuliere, STANDARD_PARAMS, type Ergebnis, type Params } from "./modell"; + +export interface Experiment { + titel: string; + beschreibung: string; + varianten: Record; +} + +const MITTE = [STANDARD_PARAMS.hoehe / 2, STANDARD_PARAMS.breite / 2] as const; + +export const EXPERIMENTE = { + wind: { + titel: "Wind", + beschreibung: "Windstärke 0 vs. 0.8, Wind nach Osten.", + varianten: { + "ohne Wind": STANDARD_PARAMS, + "Wind 0.8 nach Osten": { ...STANDARD_PARAMS, windRichtung: [1, 0], windStaerke: 0.8 }, + }, + }, + schneise: { + titel: "Brandschneise", + beschreibung: + "Wind 0.8 nach Osten, ohne vs. mit durchgehender Schneise östlich des Brandherds. " + + "Der Brandherd liegt fest in der Mitte, damit der Vergleich nicht vom zufälligen Startpunkt abhängt.", + varianten: { + "ohne Schneise": { ...STANDARD_PARAMS, windRichtung: [1, 0], windStaerke: 0.8, start: MITTE }, + "Schneise in Spalte 65": { + ...STANDARD_PARAMS, windRichtung: [1, 0], windStaerke: 0.8, start: MITTE, schneisenSpalten: [65], + }, + }, + }, + trockenheit: { + titel: "Trockenheit", + beschreibung: "Brandfaktor feucht (0.1–0.5) vs. normal (0.1–1.0) vs. trocken (0.5–1.0).", + varianten: { + "feucht (0.1–0.5)": { ...STANDARD_PARAMS, brandfaktorMin: 0.1, brandfaktorMax: 0.5 }, + "normal (0.1–1.0)": STANDARD_PARAMS, + "trocken (0.5–1.0)": { ...STANDARD_PARAMS, brandfaktorMin: 0.5, brandfaktorMax: 1.0 }, + }, + }, +} satisfies Record; + +export type ExperimentName = keyof typeof EXPERIMENTE; + +export interface Statistik { + name: string; + betroffenMittel: number; + betroffenStd: number; + dauerMittel: number; + dauerStd: number; + grossbrandAnteil: number; + /** Lauf mit dem Median der betroffenen Fläche, als Beispiel für die Grafik */ + beispiel: Ergebnis; +} + +function mittelUndStd(werte: number[]): [number, number] { + const mittel = werte.reduce((a, b) => a + b, 0) / werte.length; + const varianz = werte.reduce((a, b) => a + (b - mittel) ** 2, 0) / werte.length; + return [mittel, Math.sqrt(varianz)]; +} + +/** + * Simuliert jede Variante mit denselben Seeds. Gleiche Seeds bedeuten: alle Varianten starten mit + * demselben Wald und Brandherd, soweit die Variante die Initialisierung nicht selbst ändert. + */ +export function vergleiche( + varianten: Record, + laeufe: number, + seed: number, + fortschritt?: (fertig: number, gesamt: number) => void, +): Statistik[] { + const gesamt = Object.keys(varianten).length * laeufe; + let fertig = 0; + return Object.entries(varianten).map(([name, params]) => { + const ergebnisse: Ergebnis[] = []; + for (let i = 0; i < laeufe; i++) { + ergebnisse.push(simuliere({ ...params, seed: seed + i })); + fortschritt?.(++fertig, gesamt); + } + const anteile = ergebnisse.map((e) => e.betroffenAnteil); + const [betroffenMittel, betroffenStd] = mittelUndStd(anteile); + const [dauerMittel, dauerStd] = mittelUndStd(ergebnisse.map((e) => e.dauer)); + const sortiert = [...ergebnisse].sort((a, b) => a.betroffenAnteil - b.betroffenAnteil); + return { + name, + betroffenMittel, + betroffenStd, + dauerMittel, + dauerStd, + grossbrandAnteil: anteile.filter((a) => a > 0.5).length / laeufe, + beispiel: sortiert[Math.floor(laeufe / 2)], + }; + }); +} diff --git a/web/src/komponenten/Experimente.tsx b/web/src/komponenten/Experimente.tsx new file mode 100644 index 0000000..4cf45bf --- /dev/null +++ b/web/src/komponenten/Experimente.tsx @@ -0,0 +1,181 @@ +import { useEffect, useRef, useState } from "react"; +import { betroffen, waldflaeche } from "../modell"; +import { EXPERIMENTE, type ExperimentName, type Statistik } from "../experimente"; +import type { Auftrag, Nachricht } from "../worker"; +import Gitter from "./Gitter"; +import Legende from "./Legende"; +import Verlaufsdiagramm, { type Datenpunkt, type Serie } from "./Verlaufsdiagramm"; + +// Feste Reihenfolge: Variante i bekommt immer Farbe i +const VARIANTEN_FARBEN = ["#2a78d6", "#eb6834", "#1baf7a"]; + +const prozent = (wert: number) => `${(wert * 100).toFixed(1)} %`; + +/** Betroffene Fläche je Variante, zusammengeführt nach Zeitschritt */ +function vergleichsdaten(statistik: Statistik[]): Datenpunkt[] { + const laengste = Math.max(...statistik.map((s) => s.beispiel.dauer)); + return Array.from({ length: laengste + 1 }, (_, t) => { + const punkt: Datenpunkt = { t }; + statistik.forEach((s, i) => { + const anzahl = s.beispiel.anzahl[t]; + if (anzahl) punkt[`v${i}`] = (betroffen(anzahl) / waldflaeche(anzahl)) * 100; + }); + return punkt; + }); +} + +interface Auswertung { + experiment: ExperimentName; + laeufe: number; + statistik: Statistik[]; +} + +export default function Experimente() { + const [experiment, setExperiment] = useState("wind"); + const [laeufe, setLaeufe] = useState(20); + const [seed, setSeed] = useState(0); + const [fortschritt, setFortschritt] = useState(null); + const [auswertung, setAuswertung] = useState(null); + const [fehler, setFehler] = useState(null); + const workerRef = useRef(null); + + useEffect(() => () => workerRef.current?.terminate(), []); + + function starten() { + workerRef.current?.terminate(); + const worker = new Worker(new URL("../worker.ts", import.meta.url), { type: "module" }); + workerRef.current = worker; + setFortschritt(0); + setFehler(null); + worker.onmessage = ({ data }: MessageEvent) => { + if (data.typ === "fortschritt") { + setFortschritt(data.fertig / data.gesamt); + } else { + setAuswertung({ experiment, laeufe, statistik: data.statistik }); + setFortschritt(null); + worker.terminate(); + } + }; + worker.onerror = (e) => { + setFehler(e.message); + setFortschritt(null); + }; + worker.postMessage({ experiment, laeufe, seed } satisfies Auftrag); + } + + const serien: Serie[] = + auswertung?.statistik.map((s, i) => ({ schluessel: `v${i}`, name: s.name, farbe: VARIANTEN_FARBEN[i] })) ?? []; + + return ( +
+
+

Experiment

+
+ {(Object.keys(EXPERIMENTE) as ExperimentName[]).map((name) => ( + + ))} +
+

{EXPERIMENTE[experiment].beschreibung}

+

+ Jede Variante läuft mit denselben Seeds, startet also mit demselben Wald und Brandherd. Alle übrigen + Parameter haben ihre Standardwerte (Löschwahrscheinlichkeit 5 %, Brenndauer 2–5, 5 % natürliche Schneisen). +

+
+ + + +
+ {fortschritt !== null && } + {fehler &&

Fehler: {fehler}

} +
+ + {auswertung && ( + <> +
+

+ Ergebnis: {EXPERIMENTE[auswertung.experiment].titel} ({auswertung.laeufe} Läufe je Variante) +

+
+ + + + + + + + + + + {auswertung.statistik.map((s) => ( + + + + + + + ))} + +
Variantebetroffen (Mittel ± Std)Dauer in Schritten (Mittel ± Std)Läufe > 50 % betroffen
{s.name} + {prozent(s.betroffenMittel)} ± {prozent(s.betroffenStd)} + + {s.dauerMittel.toFixed(1)} ± {s.dauerStd.toFixed(1)} + {Math.round(s.grossbrandAnteil * 100)} %
+
+
+ +
+

Typischer Lauf je Variante

+

Endzustand des Laufs mit dem Median der betroffenen Fläche.

+
+ {auswertung.statistik.map((s) => ( +
+ +
+ {s.name} +
+ betroffen {prozent(s.beispiel.betroffenAnteil)}, {s.beispiel.dauer} Schritte +
+
+ ))} +
+ +

Betroffene Fläche über die Zeit

+ +
+ + )} +
+ ); +} diff --git a/web/src/komponenten/Gitter.tsx b/web/src/komponenten/Gitter.tsx new file mode 100644 index 0000000..dfa8535 --- /dev/null +++ b/web/src/komponenten/Gitter.tsx @@ -0,0 +1,66 @@ +import { useEffect, useRef, type PointerEvent } from "react"; +import { ZUSTAENDE, type Zelle } from "../modell"; + +// Zustandsfarben als RGB, einmal vorberechnet +const FARBEN_RGB = ZUSTAENDE.map(({ farbe }) => [1, 3, 5].map((i) => parseInt(farbe.slice(i, i + 2), 16))); + +interface Props { + breite: number; + hoehe: number; + zustand: Uint8Array; + /** Erhöhen, um neu zu zeichnen, wenn das Gitter direkt verändert wurde */ + version?: number; + /** Wird beim Klicken und Ziehen mit der Zelle unter dem Zeiger aufgerufen */ + onZelle?: (zelle: Zelle) => void; + beschriftung: string; +} + +export default function Gitter({ breite, hoehe, zustand, version, onZelle, beschriftung }: Props) { + const canvasRef = useRef(null); + const maltRef = useRef(false); + + useEffect(() => { + const ctx = canvasRef.current?.getContext("2d"); + if (!ctx) return; + const bild = ctx.createImageData(breite, hoehe); + for (let i = 0; i < zustand.length; i++) { + const [r, g, b] = FARBEN_RGB[zustand[i]]; + bild.data[4 * i] = r; + bild.data[4 * i + 1] = g; + bild.data[4 * i + 2] = b; + bild.data[4 * i + 3] = 255; + } + ctx.putImageData(bild, 0, 0); + }, [breite, hoehe, zustand, version]); + + function zelleUnterZeiger(e: PointerEvent): Zelle { + const rechteck = e.currentTarget.getBoundingClientRect(); + return [ + Math.floor(((e.clientY - rechteck.top) / rechteck.height) * hoehe), + Math.floor(((e.clientX - rechteck.left) / rechteck.width) * breite), + ]; + } + + return ( + { + if (!onZelle) return; + maltRef.current = true; + e.currentTarget.setPointerCapture(e.pointerId); + onZelle(zelleUnterZeiger(e)); + }} + onPointerMove={(e) => { + if (onZelle && maltRef.current) onZelle(zelleUnterZeiger(e)); + }} + onPointerUp={() => (maltRef.current = false)} + onPointerCancel={() => (maltRef.current = false)} + /> + ); +} diff --git a/web/src/komponenten/Legende.tsx b/web/src/komponenten/Legende.tsx new file mode 100644 index 0000000..cb6aa5a --- /dev/null +++ b/web/src/komponenten/Legende.tsx @@ -0,0 +1,14 @@ +import { ZUSTAENDE } from "../modell"; + +export default function Legende() { + return ( +
    + {ZUSTAENDE.map(({ name, farbe }) => ( +
  • + + {name} +
    • + ))} +
+ ); +} diff --git a/web/src/komponenten/Regler.tsx b/web/src/komponenten/Regler.tsx new file mode 100644 index 0000000..a19e660 --- /dev/null +++ b/web/src/komponenten/Regler.tsx @@ -0,0 +1,28 @@ +interface Props { + name: string; + wert: number; + min: number; + max: number; + schritt: number; + format?: (wert: number) => string; + onChange: (wert: number) => void; +} + +export default function Regler({ name, wert, min, max, schritt, format = String, onChange }: Props) { + return ( + + ); +} diff --git a/web/src/komponenten/Simulation.tsx b/web/src/komponenten/Simulation.tsx new file mode 100644 index 0000000..675cdb3 --- /dev/null +++ b/web/src/komponenten/Simulation.tsx @@ -0,0 +1,323 @@ +import { useCallback, useEffect, useRef, useState } from "react"; +import { + BRENNEND, + betroffen, + entzuende, + initGitter, + schritt, + setzeSchneise, + STANDARD_PARAMS, + waldflaeche, + zaehle, + zufallsgenerator, + type Gitter as GitterDaten, + type Params, + type Zelle, + type Zufall, +} from "../modell"; +import Gitter from "./Gitter"; +import Legende from "./Legende"; +import Regler from "./Regler"; +import Verlaufsdiagramm, { type Datenpunkt, type Serie } from "./Verlaufsdiagramm"; + +const WINDRICHTUNGEN: { name: string; vektor: readonly [number, number] }[] = [ + { name: "→ nach Osten", vektor: [1, 0] }, + { name: "↗ nach Nordosten", vektor: [1, 1] }, + { name: "↑ nach Norden", vektor: [0, 1] }, + { name: "↖ nach Nordwesten", vektor: [-1, 1] }, + { name: "← nach Westen", vektor: [-1, 0] }, + { name: "↙ nach Südwesten", vektor: [-1, -1] }, + { name: "↓ nach Süden", vektor: [0, -1] }, + { name: "↘ nach Südosten", vektor: [1, -1] }, +]; + +const GROESSEN = [50, 100, 150, 200]; + +const SERIEN: Serie[] = [ + { schluessel: "betroffen", name: "betroffen gesamt", farbe: "#2a78d6" }, + { schluessel: "brennend", name: "brennend", farbe: "#eb6834" }, +]; + +type Werkzeug = "schneise" | "feuer"; + +interface Lauf { + gitter: GitterDaten; + zufall: Zufall; + t: number; +} + +function messpunkt(t: number, gitter: GitterDaten): Datenpunkt { + const anzahl = zaehle(gitter.zustand); + const flaeche = waldflaeche(anzahl); + return { + t, + betroffen: (betroffen(anzahl) / flaeche) * 100, + brennend: (anzahl[BRENNEND] / flaeche) * 100, + }; +} + +const prozent = (wert: number) => `${Math.round(wert * 100)} %`; + +export default function Simulation() { + const [params, setParams] = useState({ ...STANDARD_PARAMS, seed: 1 }); + const [laeuft, setLaeuft] = useState(false); + const [tempo, setTempo] = useState(20); + const [werkzeug, setWerkzeug] = useState("schneise"); + const [verlauf, setVerlauf] = useState([]); + const [version, setVersion] = useState(0); + const laufRef = useRef(null); + // Wind und Löschwahrscheinlichkeit wirken sofort, auch während die Simulation läuft + const paramsRef = useRef(params); + paramsRef.current = params; + + function aendere(schluessel: K, wert: Params[K]) { + setParams((p) => ({ ...p, [schluessel]: wert })); + } + + // Änderungen an Parametern, die die Initialisierung betreffen, erzeugen einen neuen Wald + const { breite, hoehe, schneiseAnteil, brandfaktorMin, brandfaktorMax, brenndauerMin, brenndauerMax, seed } = params; + const neuStarten = useCallback(() => { + const zufall = zufallsgenerator(paramsRef.current.seed); + const gitter = initGitter(paramsRef.current, zufall); + laufRef.current = { gitter, zufall, t: 0 }; + setVerlauf([messpunkt(0, gitter)]); + setVersion((v) => v + 1); + setLaeuft(false); + }, []); + useEffect(neuStarten, [ + neuStarten, breite, hoehe, schneiseAnteil, brandfaktorMin, brandfaktorMax, brenndauerMin, brenndauerMax, seed, + ]); + + const einSchritt = useCallback(() => { + const lauf = laufRef.current; + if (!lauf) return; + lauf.gitter = schritt(lauf.gitter, paramsRef.current, lauf.zufall); + lauf.t += 1; + const punkt = messpunkt(lauf.t, lauf.gitter); + setVerlauf((v) => [...v, punkt]); + setVersion((v) => v + 1); + if (punkt.brennend === 0) setLaeuft(false); + }, []); + + useEffect(() => { + if (!laeuft) return; + const id = setInterval(einSchritt, 1000 / tempo); + return () => clearInterval(id); + }, [laeuft, tempo, einSchritt]); + + const onZelle = useCallback( + (zelle: Zelle) => { + const lauf = laufRef.current; + if (!lauf) return; + const geaendert = werkzeug === "schneise" ? setzeSchneise(lauf.gitter, zelle) : entzuende(lauf.gitter, zelle); + if (!geaendert) return; + const punkt = messpunkt(lauf.t, lauf.gitter); + setVerlauf((v) => [...v.slice(0, -1), punkt]); + setVersion((v) => v + 1); + }, + [werkzeug], + ); + + const lauf = laufRef.current; + const aktuell = verlauf[verlauf.length - 1]; + const brennt = aktuell !== undefined && aktuell.brennend > 0; + const brennendeZellen = lauf ? zaehle(lauf.gitter.zustand)[BRENNEND] : 0; + const status = laeuft ? "läuft" : !brennt ? "beendet" : lauf?.t === 0 ? "bereit" : "pausiert"; + const windIndex = WINDRICHTUNGEN.findIndex( + ({ vektor }) => vektor[0] === params.windRichtung[0] && vektor[1] === params.windRichtung[1], + ); + + return ( +
+
+ {lauf && ( + + )} + +
+ + + +
+ {( + [ + ["schneise", "Schneise zeichnen"], + ["feuer", "Feuer legen"], + ] as const + ).map(([wert, name]) => ( + + ))} +
+
+
+
+
Zeitschritt
+
{lauf?.t ?? 0}
+
+
+
betroffen
+
{aktuell ? aktuell.betroffen.toFixed(1) : 0} %
+
+
+
brennend
+
{brennendeZellen === 1 ? "1 Zelle" : `${brennendeZellen} Zellen`}
+
+
+
Status
+
{status}
+
+
+

+ Auf dem Gitter klicken oder ziehen, um Brandschneisen zu zeichnen oder neue Brandherde zu legen. +

+
+ +
+

Parameter

+
+ + +
+
+ +
+ aendere("seed", Math.max(0, Math.floor(Number(e.target.value))))} + /> + +
+
+ +

Wald

+ aendere("schneiseAnteil", w)} + /> + w.toFixed(2)} + onChange={(w) => setParams((p) => ({ ...p, brandfaktorMin: w, brandfaktorMax: Math.max(w, p.brandfaktorMax) }))} + /> + w.toFixed(2)} + onChange={(w) => setParams((p) => ({ ...p, brandfaktorMax: w, brandfaktorMin: Math.min(w, p.brandfaktorMin) }))} + /> + setParams((p) => ({ ...p, brenndauerMin: w, brenndauerMax: Math.max(w, p.brenndauerMax) }))} + /> + setParams((p) => ({ ...p, brenndauerMax: w, brenndauerMin: Math.min(w, p.brenndauerMin) }))} + /> + +

Während der Simulation änderbar

+
+ + +
+ w.toFixed(2)} + onChange={(w) => aendere("windStaerke", w)} + /> + aendere("loeschWahrscheinlichkeit", w)} + /> + `${w} Schritte/s`} + onChange={setTempo} + /> +
+ +
+

Verlauf

+ +
+
+ ); +} diff --git a/web/src/komponenten/Verlaufsdiagramm.tsx b/web/src/komponenten/Verlaufsdiagramm.tsx new file mode 100644 index 0000000..0142f94 --- /dev/null +++ b/web/src/komponenten/Verlaufsdiagramm.tsx @@ -0,0 +1,53 @@ +import { CartesianGrid, Legend, Line, LineChart, ResponsiveContainer, Tooltip, XAxis, YAxis } from "recharts"; + +export interface Serie { + schluessel: string; + name: string; + farbe: string; + gestrichelt?: boolean; +} + +export type Datenpunkt = { t: number } & Record; + +interface Props { + daten: Datenpunkt[]; + serien: Serie[]; +} + +/** Prozent der Waldfläche über die Zeitschritte */ +export default function Verlaufsdiagramm({ daten, serien }: Props) { + return ( +
+ + + + + + `${Number(wert).toFixed(1)} %`} + labelFormatter={(t) => `Zeitschritt ${t}`} + contentStyle={{ + background: "var(--flaeche)", + border: "1px solid var(--rand)", + borderRadius: 6, + color: "var(--text)", + }} + /> + + {serien.map((s) => ( + + ))} + + +
+ ); +} diff --git a/web/src/main.tsx b/web/src/main.tsx new file mode 100644 index 0000000..693ac2e --- /dev/null +++ b/web/src/main.tsx @@ -0,0 +1,10 @@ +import { StrictMode } from "react"; +import { createRoot } from "react-dom/client"; +import App from "./App"; +import "./styles.css"; + +createRoot(document.getElementById("root")!).render( + + + , +); diff --git a/web/src/modell.ts b/web/src/modell.ts new file mode 100644 index 0000000..a1fcb1c --- /dev/null +++ b/web/src/modell.ts @@ -0,0 +1,272 @@ +/** + * Waldbrand als zellulärer Automat – Portierung von python/ue1.py. + * + * Gleiche Regeln wie in Python, aber ein anderer Zufallsgenerator (mulberry32): + * Läufe mit demselben Seed sind reproduzierbar, stimmen aber nicht mit den Python-Läufen überein. + */ + +export const WALD = 0; +export const BRENNEND = 1; +export const ABGEBRANNT = 2; +export const GELOESCHT = 3; +export const SCHNEISE = 4; + +export const ZUSTAENDE = [ + { name: "Wald", farbe: "#008300" }, + { name: "brennend", farbe: "#e34948" }, + { name: "abgebrannt", farbe: "#3a3a38" }, + { name: "gelöscht", farbe: "#86b6ef" }, + { name: "Brandschneise", farbe: "#d9d4c7" }, +] as const; + +// Moore-Nachbarschaft: [Zeilenversatz, Spaltenversatz, Distanzgewicht] +export const NACHBARN: ReadonlyArray = [ + [-1, -1, 0.7], [-1, 0, 1.0], [-1, 1, 0.7], + [0, -1, 1.0], [0, 1, 1.0], + [1, -1, 0.7], [1, 0, 1.0], [1, 1, 0.7], +]; + +export type Zelle = readonly [zeile: number, spalte: number]; + +export interface Params { + breite: number; + hoehe: number; + /** Anteil natürlicher Brandschneisen (z.B. Wasser, Fels), zufällig verteilt */ + schneiseAnteil: number; + /** Künstliche Brandschneisen als volle Zeilen bzw. Spalten */ + schneisenZeilen: readonly number[]; + schneisenSpalten: readonly number[]; + /** Brandfaktor ("Trockenheit") je Waldzelle, gleichverteilt */ + brandfaktorMin: number; + brandfaktorMax: number; + /** Restbrenndauer je Waldzelle, ganzzahlig gleichverteilt (inklusive Grenzen) */ + brenndauerMin: number; + brenndauerMax: number; + /** (x, y): x zeigt nach Osten, y nach Norden; Richtung, in die der Wind weht */ + windRichtung: readonly [number, number]; + windStaerke: number; + loeschWahrscheinlichkeit: number; + /** Startzelle, null = zufällige Waldzelle */ + start: Zelle | null; + maxSchritte: number; + seed: number; +} + +export const STANDARD_PARAMS: Params = { + breite: 100, + hoehe: 100, + schneiseAnteil: 0.05, + schneisenZeilen: [], + schneisenSpalten: [], + brandfaktorMin: 0.1, + brandfaktorMax: 1.0, + brenndauerMin: 2, + brenndauerMax: 5, + windRichtung: [1, 0], + windStaerke: 0, + loeschWahrscheinlichkeit: 0.05, + start: null, + maxSchritte: 1000, + seed: 0, +}; + +export interface Gitter { + breite: number; + hoehe: number; + zustand: Uint8Array; + brandfaktor: Float32Array; + restbrenndauer: Uint16Array; +} + +export type Zufall = () => number; + +/** mulberry32: kleiner, schneller Zufallsgenerator mit Seed, liefert Zahlen in [0, 1) */ +export function zufallsgenerator(seed: number): Zufall { + let a = seed >>> 0; + return () => { + a = (a + 0x6d2b79f5) >>> 0; + let t = a; + t = Math.imul(t ^ (t >>> 15), t | 1); + t ^= t + Math.imul(t ^ (t >>> 7), t | 61); + return ((t ^ (t >>> 14)) >>> 0) / 4294967296; + }; +} + +/** 1 + Windstärke * cos(Winkel zwischen Windvektor und Vektor zur Nachbarzelle) */ +export function windfaktor(dr: number, dc: number, [wx, wy]: readonly [number, number], staerke: number): number { + const normWind = Math.hypot(wx, wy); + if (staerke === 0 || normWind === 0) return 1; + // Zeilenindex wächst nach unten, y zeigt nach oben + const nx = dc; + const ny = -dr; + return 1 + (staerke * (wx * nx + wy * ny)) / (normWind * Math.hypot(nx, ny)); +} + +/** Erzeugt Zustand, Brandfaktor und Restbrenndauer und entzündet die Startzelle. */ +export function initGitter(params: Params, zufall: Zufall): Gitter { + const { breite, hoehe } = params; + const n = breite * hoehe; + const zustand = new Uint8Array(n); + for (let i = 0; i < n; i++) zustand[i] = zufall() < params.schneiseAnteil ? SCHNEISE : WALD; + if (params.start) { + // Am vorgegebenen Brandherd wächst immer Wald, auch wenn dort zufällig eine natürliche Schneise läge + zustand[params.start[0] * breite + params.start[1]] = WALD; + } + for (const zeile of params.schneisenZeilen) zustand.fill(SCHNEISE, zeile * breite, (zeile + 1) * breite); + for (const spalte of params.schneisenSpalten) { + for (let r = 0; r < hoehe; r++) zustand[r * breite + spalte] = SCHNEISE; + } + // Rand: die äußerste Zeile bzw. Spalte auf jeder Seite ist Brandschneise + zustand.fill(SCHNEISE, 0, breite); + zustand.fill(SCHNEISE, (hoehe - 1) * breite, n); + for (let r = 0; r < hoehe; r++) { + zustand[r * breite] = SCHNEISE; + zustand[r * breite + breite - 1] = SCHNEISE; + } + + let start: number; + if (params.start === null) { + // Zufällige Waldzelle; hängt nur vom Seed und den Zelltypen ab, daher bei gleichem Seed + // in allen Varianten dieselbe, solange diese die Zelltypen nicht verändern + const waldzellen: number[] = []; + for (let i = 0; i < n; i++) if (zustand[i] === WALD) waldzellen.push(i); + if (waldzellen.length === 0) throw new Error("Keine Waldzelle für den Brandherd vorhanden"); + start = waldzellen[Math.floor(zufall() * waldzellen.length)]; + } else { + start = params.start[0] * breite + params.start[1]; + if (zustand[start] !== WALD) { + throw new Error(`Startzelle (${params.start.join(", ")}) liegt auf einer künstlichen Brandschneise oder am Rand`); + } + } + + const brandfaktor = new Float32Array(n); + const restbrenndauer = new Uint16Array(n); + const spanne = params.brandfaktorMax - params.brandfaktorMin; + const dauern = params.brenndauerMax - params.brenndauerMin + 1; + for (let i = 0; i < n; i++) { + // Für jede Zelle ziehen, damit Varianten mit gleichem Seed denselben Wald erhalten + const bf = params.brandfaktorMin + zufall() * spanne; + const dauer = params.brenndauerMin + Math.floor(zufall() * dauern); + if (zustand[i] !== SCHNEISE) { + brandfaktor[i] = bf; + restbrenndauer[i] = dauer; + } + } + + zustand[start] = BRENNEND; + return { breite, hoehe, zustand, brandfaktor, restbrenndauer }; +} + +/** Ein synchroner Zeitschritt: liest nur das alte Gitter und gibt ein neues zurück. */ +export function schritt(gitter: Gitter, params: Params, zufall: Zufall): Gitter { + const { breite, hoehe, zustand, brandfaktor } = gitter; + const neu: Gitter = { + breite, + hoehe, + zustand: zustand.slice(), + brandfaktor: brandfaktor.slice(), + restbrenndauer: gitter.restbrenndauer.slice(), + }; + const windfaktoren = NACHBARN.map(([dr, dc]) => windfaktor(dr, dc, params.windRichtung, params.windStaerke)); + + for (let r = 0; r < hoehe; r++) { + for (let c = 0; c < breite; c++) { + const i = r * breite + c; + if (zustand[i] !== BRENNEND) continue; + + if (zufall() < params.loeschWahrscheinlichkeit) { + neu.zustand[i] = GELOESCHT; + neu.brandfaktor[i] = 0; + neu.restbrenndauer[i] = 0; + continue; + } + + for (let k = 0; k < NACHBARN.length; k++) { + const [dr, dc, gewicht] = NACHBARN[k]; + const nr = r + dr; + const nc = c + dc; + if (nr < 0 || nr >= hoehe || nc < 0 || nc >= breite) continue; + const j = nr * breite + nc; + if (zustand[j] !== WALD) continue; + if (zufall() < 0.5 * gewicht * brandfaktor[j] * windfaktoren[k]) neu.zustand[j] = BRENNEND; + } + + neu.restbrenndauer[i] -= 1; + if (neu.restbrenndauer[i] === 0) { + neu.zustand[i] = ABGEBRANNT; + neu.brandfaktor[i] = 0; + } + } + } + return neu; +} + +export type Anzahl = number[]; + +export function zaehle(zustand: Uint8Array): Anzahl { + const anzahl = new Array(ZUSTAENDE.length).fill(0); + for (const z of zustand) anzahl[z]++; + return anzahl; +} + +/** Zellen, die irgendwann gebrannt haben */ +export function betroffen(anzahl: Anzahl): number { + return anzahl[BRENNEND] + anzahl[ABGEBRANNT] + anzahl[GELOESCHT]; +} + +/** Jede Zelle, die keine Brandschneise ist, war zu Beginn Wald */ +export function waldflaeche(anzahl: Anzahl): number { + return anzahl.reduce((a, b) => a + b, 0) - anzahl[SCHNEISE]; +} + +export interface Ergebnis { + breite: number; + hoehe: number; + endzustand: Uint8Array; + /** Anzahl Zellen je Zustand und Zeitschritt, anzahl[0] = Anfangszustand */ + anzahl: Anzahl[]; + dauer: number; + betroffenAnteil: number; +} + +/** Simuliert, bis keine Zelle mehr brennt oder maxSchritte erreicht ist. */ +export function simuliere(params: Params): Ergebnis { + const zufall = zufallsgenerator(params.seed); + let gitter = initGitter(params, zufall); + const anzahl = [zaehle(gitter.zustand)]; + while (anzahl[anzahl.length - 1][BRENNEND] > 0 && anzahl.length <= params.maxSchritte) { + gitter = schritt(gitter, params, zufall); + anzahl.push(zaehle(gitter.zustand)); + } + const letzte = anzahl[anzahl.length - 1]; + return { + breite: gitter.breite, + hoehe: gitter.hoehe, + endzustand: gitter.zustand, + anzahl, + dauer: anzahl.length - 1, + betroffenAnteil: betroffen(letzte) / waldflaeche(letzte), + }; +} + +function imInneren(gitter: Gitter, [r, c]: Zelle): boolean { + return r > 0 && r < gitter.hoehe - 1 && c > 0 && c < gitter.breite - 1; +} + +/** Macht eine Waldzelle zur Brandschneise (interaktives Zeichnen). Verändert das Gitter direkt. */ +export function setzeSchneise(gitter: Gitter, zelle: Zelle): boolean { + const i = zelle[0] * gitter.breite + zelle[1]; + if (!imInneren(gitter, zelle) || gitter.zustand[i] !== WALD) return false; + gitter.zustand[i] = SCHNEISE; + gitter.brandfaktor[i] = 0; + gitter.restbrenndauer[i] = 0; + return true; +} + +/** Entzündet eine Waldzelle (interaktiv). Verändert das Gitter direkt. */ +export function entzuende(gitter: Gitter, zelle: Zelle): boolean { + const i = zelle[0] * gitter.breite + zelle[1]; + if (!imInneren(gitter, zelle) || gitter.zustand[i] !== WALD) return false; + gitter.zustand[i] = BRENNEND; + return true; +} diff --git a/web/src/styles.css b/web/src/styles.css new file mode 100644 index 0000000..32b9c08 --- /dev/null +++ b/web/src/styles.css @@ -0,0 +1,403 @@ +:root { + color-scheme: light; + --hintergrund: #f4f3f0; + --flaeche: #fcfcfb; + --text: #0b0b0b; + --text-2: #52514e; + --rand: #dcdad4; + --raster: #e6e4df; + --akzent: #2a78d6; + --akzent-text: #ffffff; + --fehler: #c62828; + font-family: system-ui, -apple-system, "Segoe UI", Roboto, sans-serif; + line-height: 1.5; +} + +@media (prefers-color-scheme: dark) { + :root { + color-scheme: dark; + --hintergrund: #121211; + --flaeche: #1a1a19; + --text: #f0efec; + --text-2: #c3c2b7; + --rand: #34332f; + --raster: #2a2a28; + --akzent: #3987e5; + --fehler: #ef7b7b; + } +} + +* { + box-sizing: border-box; +} + +body { + margin: 0; + background: var(--hintergrund); + color: var(--text); +} + +#root { + max-width: 1280px; + margin: 0 auto; + padding: 16px; +} + +[hidden] { + display: none !important; +} + +h1, +h2, +h3 { + margin: 0 0 12px; + line-height: 1.25; +} + +h1 { + font-size: 1.5rem; +} + +h2 { + font-size: 1.1rem; +} + +h3 { + font-size: 0.95rem; + margin-top: 20px; + color: var(--text-2); +} + +p { + margin: 0 0 12px; +} + +.kopf { + display: flex; + flex-wrap: wrap; + align-items: end; + justify-content: space-between; + gap: 12px; + margin-bottom: 16px; +} + +.kopf p { + margin: 0; + color: var(--text-2); +} + +.reiter, +.werkzeug, +.experiment-wahl { + display: inline-flex; + border: 1px solid var(--rand); + border-radius: 8px; + overflow: hidden; + background: var(--flaeche); +} + +.experiment-wahl { + margin-bottom: 12px; +} + +.reiter__tab, +.werkzeug__option { + border: 0; + background: transparent; + color: var(--text); + padding: 8px 14px; + font: inherit; + cursor: pointer; +} + +.reiter__tab + .reiter__tab, +.werkzeug__option + .werkzeug__option { + border-left: 1px solid var(--rand); +} + +.reiter__tab.aktiv, +.werkzeug__option.aktiv { + background: var(--akzent); + color: var(--akzent-text); +} + +.karte { + background: var(--flaeche); + border: 1px solid var(--rand); + border-radius: 12px; + padding: 16px; + min-width: 0; +} + +.simulation { + display: grid; + grid-template-columns: minmax(0, 1fr) 320px; + grid-template-areas: + "gitter parameter" + "verlauf parameter"; + gap: 16px; + align-items: start; +} + +.simulation__gitter { + grid-area: gitter; +} + +.simulation__parameter { + grid-area: parameter; +} + +.simulation__verlauf { + grid-area: verlauf; +} + +@media (max-width: 860px) { + .simulation { + grid-template-columns: minmax(0, 1fr); + grid-template-areas: "gitter" "parameter" "verlauf"; + } +} + +.experimente { + display: grid; + gap: 16px; +} + +.gitter { + display: block; + width: 100%; + max-width: 640px; + margin: 0 auto; + image-rendering: pixelated; + border-radius: 4px; +} + +.gitter--interaktiv { + cursor: crosshair; + touch-action: none; +} + +.legende { + display: flex; + flex-wrap: wrap; + justify-content: center; + gap: 4px 16px; + list-style: none; + padding: 0; + margin: 12px 0; + font-size: 0.875rem; + color: var(--text-2); +} + +.legende li { + display: flex; + align-items: center; + gap: 6px; +} + +.legende__farbe { + width: 12px; + height: 12px; + border-radius: 3px; + outline: 1px solid var(--rand); +} + +.steuerung { + display: flex; + flex-wrap: wrap; + align-items: end; + gap: 8px; + margin-bottom: 12px; +} + +.steuerung .werkzeug { + margin-left: auto; +} + +.knopf { + border: 1px solid var(--rand); + background: var(--flaeche); + color: var(--text); + border-radius: 8px; + padding: 8px 14px; + font: inherit; + cursor: pointer; +} + +.knopf:disabled { + opacity: 0.5; + cursor: default; +} + +.knopf--primaer { + background: var(--akzent); + border-color: var(--akzent); + color: var(--akzent-text); + min-width: 88px; +} + +.kennzahlen { + display: grid; + grid-template-columns: repeat(auto-fit, minmax(110px, 1fr)); + gap: 8px; + margin: 0 0 12px; +} + +.kennzahlen div { + border: 1px solid var(--rand); + border-radius: 8px; + padding: 8px 12px; +} + +.kennzahlen dt { + font-size: 0.8rem; + color: var(--text-2); +} + +.kennzahlen dd { + margin: 0; + font-size: 1.15rem; + font-variant-numeric: tabular-nums; +} + +.hinweis { + font-size: 0.875rem; + color: var(--text-2); +} + +.feld { + display: grid; + gap: 4px; + margin-bottom: 12px; + font-size: 0.9rem; +} + +.feld--inline { + margin-bottom: 0; +} + +.feld__zeile { + display: flex; + gap: 8px; +} + +.feld__zeile input { + flex: 1; + min-width: 0; +} + +input[type="number"], +select { + font: inherit; + color: var(--text); + background: var(--flaeche); + border: 1px solid var(--rand); + border-radius: 8px; + padding: 7px 10px; +} + +.feld--inline input { + width: 110px; +} + +.regler { + display: grid; + gap: 2px; + margin-bottom: 10px; + font-size: 0.9rem; +} + +.regler__kopf { + display: flex; + justify-content: space-between; +} + +.regler output { + color: var(--text-2); + font-variant-numeric: tabular-nums; +} + +.regler input { + width: 100%; + accent-color: var(--akzent); +} + +progress { + width: 100%; + accent-color: var(--akzent); +} + +.fehler { + color: var(--fehler); +} + +.tabelle-rahmen { + overflow-x: auto; +} + +table { + width: 100%; + border-collapse: collapse; + font-variant-numeric: tabular-nums; +} + +th, +td { + text-align: left; + padding: 8px 12px; + border-bottom: 1px solid var(--rand); + white-space: nowrap; +} + +th { + font-size: 0.85rem; + font-weight: 600; + color: var(--text-2); +} + +.beispiele { + display: grid; + grid-template-columns: repeat(auto-fit, minmax(200px, 1fr)); + gap: 16px; +} + +.beispiele figure { + margin: 0; +} + +.beispiele .gitter { + max-width: 400px; +} + +.beispiele figcaption { + margin-top: 8px; + font-size: 0.875rem; + text-align: center; + color: var(--text-2); +} + +.beispiele strong { + color: var(--text); +} + +/* Recharts zeichnet SVG; Farben über CSS, damit sie dem Farbschema folgen */ +.diagramm .recharts-cartesian-grid line { + stroke: var(--raster); +} + +.diagramm .recharts-cartesian-axis-line { + stroke: var(--rand); +} + +.diagramm .recharts-text { + fill: var(--text-2); + font-size: 12px; +} + +.diagramm .recharts-legend-item-text { + color: var(--text) !important; +} + +.diagramm .recharts-tooltip-cursor { + stroke: var(--text-2); +} diff --git a/web/src/worker.ts b/web/src/worker.ts new file mode 100644 index 0000000..2815ddf --- /dev/null +++ b/web/src/worker.ts @@ -0,0 +1,25 @@ +// Führt Experimente im Hintergrund aus, damit die Oberfläche bedienbar bleibt +import { EXPERIMENTE, vergleiche, type ExperimentName, type Statistik } from "./experimente"; + +export interface Auftrag { + experiment: ExperimentName; + laeufe: number; + seed: number; +} + +export type Nachricht = + | { typ: "fortschritt"; fertig: number; gesamt: number } + | { typ: "ergebnis"; statistik: Statistik[] }; + +// Die Typen der DOM-Bibliothek beschreiben ein Fenster, nicht einen Worker +const kanal = self as unknown as { + onmessage: ((e: MessageEvent) => void) | null; + postMessage(nachricht: Nachricht): void; +}; + +kanal.onmessage = ({ data: { experiment, laeufe, seed } }) => { + const statistik = vergleiche(EXPERIMENTE[experiment].varianten, laeufe, seed, (fertig, gesamt) => + kanal.postMessage({ typ: "fortschritt", fertig, gesamt }), + ); + kanal.postMessage({ typ: "ergebnis", statistik }); +}; diff --git a/web/tsconfig.json b/web/tsconfig.json new file mode 100644 index 0000000..4f83ff6 --- /dev/null +++ b/web/tsconfig.json @@ -0,0 +1,17 @@ +{ + "compilerOptions": { + "target": "ES2022", + "lib": ["ES2023", "DOM", "DOM.Iterable"], + "module": "ESNext", + "moduleResolution": "bundler", + "jsx": "react-jsx", + "types": ["vite/client"], + "strict": true, + "noUnusedLocals": true, + "noUnusedParameters": true, + "noEmit": true, + "isolatedModules": true, + "skipLibCheck": true + }, + "include": ["src", "vite.config.ts"] +} diff --git a/web/vite.config.ts b/web/vite.config.ts new file mode 100644 index 0000000..7c52c50 --- /dev/null +++ b/web/vite.config.ts @@ -0,0 +1,8 @@ +import { defineConfig } from "vite"; +import react from "@vitejs/plugin-react"; + +export default defineConfig({ + // Relative Pfade, damit die App auch unter einem Unterpfad wie /ue1 läuft + base: "./", + plugins: [react()], +});