binary-anchor-model/bam_simulator.py at main · nobudy-bot/binary-anchor-model · GitHub

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import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns

'''
Binary Anchor Model (BAM) V2.0 - Figure Reproduction Script (Baseline)
========================================================================
This script is specifically designed to reproduce Figure 4 and Figure 5
from the preprint: "The Binary Anchor: Cognition, Symbolic Loops, and Systems Failure".

* Academic Note for Reviewers:
In this visual demonstration script, the environmental variables (m_t and r_t)
are intentionally driven by sinusoidal functions to cleanly illustrate the
phase transitions and cyclic dynamics for the paper's figures.
For the strict, endogenously calculated mathematical engine without forced waves,
please run `bam_engine.py` (Option A).

Author: Norimitsu Sawada (Independent Researcher)
'''

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def run_simulation(T=200, eta_A0=0.05, theta=10.0, seed=42):
    np.random.seed(seed)
    t = np.arange(T)

    # m_t: Biological needs (System A signals)
    m_t = 0.5 + 0.3 * np.sin(2 * np.pi * t / 60) + np.random.normal(0, 0.02, T)

    # m_sys: Social life maintenance (System B signals)
    m_sys = np.full(T, 0.8)
    m_sys[120:] = 0.3 # Shift in social expectation at t=120

    # Initialization
    H = np.zeros(T)
    A = np.zeros(T)
    V = np.zeros(T)
    r = np.zeros(T)
    bursts = []

    h_current = 0
    for i in range(T):
        # r_t: Responsibility allocation (tension parameter)
        r_val = 0.7 + 0.2 * np.cos(2 * np.pi * i / 100)
        r[i] = r_val

        # Master Equation: V_t = r*m + (1-r)*m_sys
        v_val = r_val * m_t[i] + (1 - r_val) * m_sys[i]
        V[i] = v_val

        # WTA Decision
        A[i] = 1 if v_val > 0.5 else 0

        # Hesitation Energy (H_t) calculation
        # delta_t: Divergence between System A and System B
        delta = abs(m_t[i] - m_sys[i])

        # H_t accumulation logic with recovery (eta_A0)
        h_current = max(0, h_current + r_val * delta - eta_A0)

        # Burst event (Threshold theta)
        if h_current > theta:
            bursts.append(i)
            h_current = h_current * 0.1 # Partial discharge after burst

        H[i] = h_current

    return pd.DataFrame({'t': t, 'm_t': m_t, 'm_sys': m_sys, 'V_t': V, 'H_t': H, 'A_t': A}), bursts

def plot_results(df, bursts, filename='bam_simulation_result.png'):
    sns.set_theme(style="whitegrid")
    fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10), sharex=True)

    # Plot 1: Components of the Master Equation
    ax1.plot(df['t'], df['m_t'], label='Bio Need (m_t)', color='green', alpha=0.5)
    ax1.plot(df['t'], df['m_sys'], label='Social Demand (m_sys)', color='blue', linestyle='--')
    ax1.plot(df['t'], df['V_t'], label='WTA Argument (V_t)', color='black', linewidth=2)
    ax1.axhline(0.5, color='red', linestyle=':', label='WTA Threshold')
    ax1.set_title("BAM V2.0: Master Equation Dynamics")
    ax1.legend(loc='upper right')

    # Plot 2: Hesitation Energy and Bursts
    ax2.plot(df['t'], df['H_t'], label='Hesitation Energy (H_t)', color='purple')
    ax2.axhline(10.0, color='darkred', linestyle='--', label='Burst Threshold (theta)')
    for b in bursts:
        ax2.axvline(b, color='orange', alpha=0.3)
    ax2.set_title("BAM V2.0: Hesitation Energy Accumulation")
    ax2.set_xlabel("Time (t)")
    ax2.legend(loc='upper right')

    plt.tight_layout()
    plt.savefig(filename)
    print(f"Plot saved as {filename}")

if __name__ == "__main__":
    # Simulate Resilient (High eta_A0) vs Vulnerable (Low eta_A0)
    print("Running BAM simulations...")
    df_res, b_res = run_simulation(eta_A0=0.10)
    df_vul, b_vul = run_simulation(eta_A0=0.02)

    plot_results(df_vul, b_vul, 'bam_simulation_vulnerable.png')

    # Comparison Plot
    plt.figure(figsize=(10, 6))
    plt.plot(df_vul['t'], df_vul['H_t'], 'r', label='Vulnerable (Low eta_A0)')
    plt.plot(df_res['t'], df_res['H_t'], 'b', label='Resilient (High eta_A0)')
    plt.axhline(10.0, color='black', linestyle='--', label='Burst Threshold')
    plt.title("BAM: Impact of Amygdala Plasticity (eta_A0) on Energy Accumulation")
    plt.xlabel("Time (t)")
    plt.ylabel("Hesitation Energy (H_t)")
    plt.legend()
    plt.savefig('bam_comparison_eta.png')
    print("Comparison plot saved.")