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app.py
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# boids_streamlit_advanced.py
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import streamlit as st
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import numpy as np
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import plotly.graph_objects as go
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import time
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# Boidクラスの定義
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class Boid:
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def __init__(self, position, velocity):
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self.position = np.array(position, dtype='float64')
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self.velocity = np.array(velocity, dtype='float64')
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self.acceleration = np.zeros(2, dtype='float64')
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self.history = []
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def update(self, boids, width, height, params):
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self.flock(boids, params)
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self.velocity += self.acceleration
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speed = np.linalg.norm(self.velocity)
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if speed > params['max_speed']:
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self.velocity = (self.velocity / speed) * params['max_speed']
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self.position += self.velocity
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self.acceleration = np.zeros(2, dtype='float64')
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# 画面端でのラッピング
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self.position[0] = self.position[0] % width
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self.position[1] = self.position[1] % height
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# 履歴に現在の位置を追加
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if params['draw_trail']:
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self.history.append(self.position.copy())
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if len(self.history) > params['max_history']:
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self.history.pop(0)
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def flock(self, boids, params):
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self.acceleration = np.zeros(2, dtype='float64')
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self.fly_towards_center(boids, params)
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self.avoid_others(boids, params)
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self.match_velocity(boids, params)
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self.limit_speed(params)
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self.avoid_boundaries(width=params['width'], height=params['height'], params=params)
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def fly_towards_center(self, boids, params):
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centering_factor = params['centering_factor']
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center_x = 0.0
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center_y = 0.0
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num_neighbors = 0
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for other in boids:
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if other is not self and self.distance(other) < params['visual_range']:
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center_x += other.position[0]
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center_y += other.position[1]
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num_neighbors += 1
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if num_neighbors > 0:
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center_x /= num_neighbors
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center_y /= num_neighbors
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direction = np.array([center_x, center_y]) - self.position
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self.acceleration += centering_factor * direction
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def avoid_others(self, boids, params):
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min_distance = params['min_distance']
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avoid_factor = params['avoid_factor']
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move = np.zeros(2, dtype='float64')
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for other in boids:
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if other is not self and self.distance(other) < min_distance:
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move += self.position - other.position
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if np.linalg.norm(move) > 0:
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move = move / np.linalg.norm(move) * avoid_factor
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self.acceleration += move
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def match_velocity(self, boids, params):
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matching_factor = params['matching_factor']
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avg_velocity = np.zeros(2, dtype='float64')
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num_neighbors = 0
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for other in boids:
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if other is not self and self.distance(other) < params['visual_range']:
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avg_velocity += other.velocity
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num_neighbors += 1
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if num_neighbors > 0:
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avg_velocity /= num_neighbors
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self.acceleration += matching_factor * (avg_velocity - self.velocity)
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def limit_speed(self, params):
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speed = np.linalg.norm(self.velocity)
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if speed > params['max_speed']:
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self.velocity = (self.velocity / speed) * params['max_speed']
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def avoid_boundaries(self, width, height, params):
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margin = params['boundary_margin']
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turn_factor = params['boundary_turn_factor']
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if self.position[0] < margin:
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self.acceleration[0] += turn_factor
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elif self.position[0] > width - margin:
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self.acceleration[0] -= turn_factor
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if self.position[1] < margin:
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self.acceleration[1] += turn_factor
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elif self.position[1] > height - margin:
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self.acceleration[1] -= turn_factor
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def distance(self, other):
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return np.linalg.norm(self.position - other.position)
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# シミュレーションパラメータ
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params = {
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'num_boids': 100,
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'visual_range': 75.0,
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'min_distance': 20.0,
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'centering_factor': 0.005,
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'avoid_factor': 0.05,
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'matching_factor': 0.05,
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'max_speed': 15.0,
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'draw_trail': False,
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'max_history': 50,
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'width': 800,
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'height': 600,
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'boundary_margin': 100.0,
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'boundary_turn_factor': 0.05
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}
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# Streamlitのサイドバーでパラメータを調整
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st.sidebar.title("Boids Simulation Parameters")
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params['num_boids'] = st.sidebar.slider("Number of Boids", 10, 300, 100)
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params['visual_range'] = st.sidebar.slider("Visual Range", 10.0, 200.0, 75.0)
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params['min_distance'] = st.sidebar.slider("Minimum Separation Distance", 5.0, 100.0, 20.0)
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params['centering_factor'] = st.sidebar.slider("Centering Factor", 0.001, 0.02, 0.005)
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params['avoid_factor'] = st.sidebar.slider("Avoidance Factor", 0.01, 0.1, 0.05)
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params['matching_factor'] = st.sidebar.slider("Matching Factor", 0.01, 0.1, 0.05)
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params['max_speed'] = st.sidebar.slider("Maximum Speed", 5.0, 30.0, 15.0)
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params['draw_trail'] = st.sidebar.checkbox("Draw Trails")
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if params['draw_trail']:
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params['max_history'] = st.sidebar.slider("Trail Length", 10, 100, 50)
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params['boundary_margin'] = st.sidebar.slider("Boundary Margin", 50.0, 300.0, 100.0)
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params['boundary_turn_factor'] = st.sidebar.slider("Boundary Turn Factor", 0.01, 0.2, 0.05)
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# シミュレーション画面サイズ
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width, height = 800, 600
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params['width'] = width
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params['height'] = height
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# Boidsの初期化
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boids = []
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for _ in range(params['num_boids']):
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position = [np.random.uniform(0, width), np.random.uniform(0, height)]
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angle = np.random.uniform(0, 2 * np.pi)
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velocity = [np.cos(angle), np.sin(angle)]
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boids.append(Boid(position, velocity))
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# Plotlyのグラフ設定
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fig = go.Figure(
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layout=go.Layout(
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xaxis=dict(range=[0, width], autorange=False, showgrid=False, zeroline=False),
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yaxis=dict(range=[0, height], autorange=False, showgrid=False, zeroline=False),
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width=width,
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height=height,
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margin=dict(l=0, r=0, t=0, b=0)
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)
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)
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# Boidsの初期位置をプロット
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scatter = go.Scatter(
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x=[boid.position[0] for boid in boids],
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y=[boid.position[1] for boid in boids],
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mode='markers',
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marker=dict(size=8, color='blue')
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)
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fig.add_trace(scatter)
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# トレイル用のトレース
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if params['draw_trail']:
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trail_scatter = go.Scatter(
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x=[],
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y=[],
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mode='lines',
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line=dict(color='rgba(0,0,255,0.2)', width=1),
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showlegend=False
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)
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fig.add_trace(trail_scatter)
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# Streamlitのタイトル
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st.title("Boids Simulation with Streamlit and Plotly")
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# 説明セクション
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st.header("群れアルゴリズムBoidsの数学的背景")
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st.markdown(r"""
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### **Boidsアルゴリズムの概要**
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Boidsアルゴリズムは、Craig Reynoldsによって1986年に提案された群れ行動のシミュレーション手法です。各エージェント(Boid)は単純なルールに従うことで、複雑な群れ行動を再現します。基本的な3つのルールは以下の通りです:
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1. **分離(Separation)**: 隣接するBoidから適切な距離を保ち、衝突を避ける。
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2. **整列(Alignment)**: 隣接するBoidの平均速度に自身の速度を合わせる。
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3. **結合(Cohesion)**: 隣接するBoidの中心に向かって移動する。
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### **数式によるモデルの定義**
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Boidsの動作は、各エージェントの位置ベクトル \(\mathbf{p}_i(t)\) と速度ベクトル \(\mathbf{v}_i(t)\) で表されます。時間 \(t\) におけるエージェント \(i\) の位置と速度は、以下の微分方程式で記述されます:
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\[
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\frac{d\mathbf{p}_i(t)}{dt} = \mathbf{v}_i(t)
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\]
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\[
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\frac{d\mathbf{v}_i(t)}{dt} = \mathbf{a}_i(t)
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\]
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ここで、加速度 \(\mathbf{a}_i(t)\) は以下の3つの力の合成です:
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\[
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\mathbf{a}_i(t) = \mathbf{a}_{\text{separation}} + \mathbf{a}_{\text{alignment}} + \mathbf{a}_{\text{cohesion}}
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\]
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#### **1. 分離(Separation)**
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Boidが他のBoidと衝突しないようにするための力。エージェント \(i\) と近傍エージェント \(j\) との間の距離を \(d_{ij}\) とすると、分離力 \(\mathbf{a}_{\text{separation}}\) は以下のように定義されます:
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\[
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\mathbf{a}_{\text{separation}} = \sum_{j \in N(i)} \frac{\mathbf{p}_i - \mathbf{p}_j}{d_{ij}^2}
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\]
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ここで、\(N(i)\) はBoid \(i\) の近傍にいるBoidの集合です。
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#### **2. 整列(Alignment)**
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Boidが周囲のBoidと同じ方向に移動するようにするための力。近傍Boidの平均速度 \(\mathbf{v}_{\text{avg}}\) を計算し、Boid \(i\) の速度をそれに合わせるための力は以下の通りです:
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\[
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\mathbf{a}_{\text{alignment}} = \frac{\mathbf{v}_{\text{avg}} - \mathbf{v}_i}{\tau}
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\]
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ここで、\(\tau\) は調整パラメータです。
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#### **3. 結合(Cohesion)**
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Boidが周囲のBoidの中心に向かって移動するようにするための力。近傍Boidの中心 \(\mathbf{C}_{\text{avg}}\) を計算し、Boid \(i\) がそこに向かうための力は以下の通りです:
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\[
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\mathbf{a}_{\text{cohesion}} = \frac{\mathbf{C}_{\text{avg}} - \mathbf{p}_i}{\sigma}
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\]
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ここで、\(\sigma\) は調整パラメータです。
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### **アルゴリズムの更新ルール**
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各Boidの位置と速度は、離散的な時間ステップ \( \Delta t \) に基づいて更新されます。更新ルールは以下のようになります:
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\[
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\mathbf{v}_i(t + \Delta t) = \mathbf{v}_i(t) + \mathbf{a}_i(t) \Delta t
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\]
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\[
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\mathbf{p}_i(t + \Delta t) = \mathbf{p}_i(t) + \mathbf{v}_i(t + \Delta t) \Delta t
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\]
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これらの式に基づき、各Boidは分離、整列、結合の力を計算し、それに基づいて速度と位置を更新します。
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### **追加機能の説明**
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本シミュレーションでは、以下の追加機能を���装しています:
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1. **境界回避(Boundary Avoidance)**: シミュレーション領域の端にBoidが近づくと、Boidが逆方向に加速度を受けて領域内に留まるようにします。これにより、Boidが画面外に出ることを防ぎます。
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2. **トレイル描画(Trail Drawing)**: Boidの過去の位置をトレイルとして表示し、動きの軌跡を視覚化します。これにより、Boidの動きのパターンを追跡することが容易になります。
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### **パラメータの追加とその役割**
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- **Boundary Margin (\(M\))**: シミュレーション領域の端からBoidが回避を開始する距離。
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- **Boundary Turn Factor (\(\gamma\))**: 境界回避力の強さを調整する係数。
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これらのパラメータにより、Boidが領域の端に近づいた際の挙動を細かく制御できます。
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""")
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# アニメーションの表示領域
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animation_placeholder = st.empty()
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# アニメーションの実行
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frame_rate = 30 # フレームレート (FPS)
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sleep_time = 1.0 / frame_rate
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# リセットボタンの追加
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if st.sidebar.button("Reset Simulation"):
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boids = []
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for _ in range(params['num_boids']):
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position = [np.random.uniform(0, width), np.random.uniform(0, height)]
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angle = np.random.uniform(0, 2 * np.pi)
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velocity = [np.cos(angle), np.sin(angle)]
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boids.append(Boid(position, velocity))
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# アニメーションの実行ループ
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while True:
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# Boidsの更新
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for boid in boids:
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boid.update(boids, width, height, params)
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# Boidsの位置データを更新
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scatter.x = [boid.position[0] for boid in boids]
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scatter.y = [boid.position[1] for boid in boids]
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# トレイルの更新
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if params['draw_trail']:
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trail_x = []
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trail_y = []
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for boid in boids:
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trail_x.extend([pos[0] for pos in boid.history])
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trail_y.extend([pos[1] for pos in boid.history])
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trail_scatter.x = trail_x
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trail_scatter.y = trail_y
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# グラフの更新
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fig.data[0].x = scatter.x
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fig.data[0].y = scatter.y
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if params['draw_trail']:
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fig.data[1].x = trail_scatter.x
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fig.data[1].y = trail_scatter.y
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# アニメーション表示
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animation_placeholder.plotly_chart(fig, use_container_width=True)
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# フレームレート調整
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time.sleep(sleep_time)
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