bitcoin price model

bitcoin-price-model.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d

# --- Parameters ---
k = 0.48
peak_value = 115000
t0 = 2025
A = peak_value * 4 / k  # Ensures derivative sigmoid peaks at 115K

# Time vector
t = np.linspace(2005, 2045, 1000)

# Sigmoid and its derivative
def sigmoid(t): 
    return A / (1 + np.exp(-k * (t - t0)))

def d_sigmoid(t): 
    return (A * k * np.exp(-k * (t - t0))) / ((1 + np.exp(-k * (t - t0)))**2)

y_sigmoid = sigmoid(t)
y_derivative = d_sigmoid(t)

# --- Log-shaped BTC price with chaos ---
x = (t - t0) / 5
log_like = np.exp(-0.5 * x**2)

np.random.seed(42)
noise = np.random.normal(0, 0.15, size=len(t))
btc_raw = log_like * (1 + noise)

# Normalize to price range
price_min, price_max = 1, peak_value
btc_scaled = price_min + (btc_raw - btc_raw.min()) / (btc_raw.max() - btc_raw.min()) * (price_max - price_min)

# --- Anchor point correction ---
anchor_years = np.array([2010, 2013, 2017, 2018, 2021, 2022, 2025])
anchor_prices = np.array([0.1, 1000, 20000, 3000, 60000, 16000, 115000])
anchor_interp = interp1d(anchor_years, anchor_prices, kind='linear', fill_value='extrapolate')
anchor_curve = anchor_interp(t)

# Blend anchors into the curve
btc_price = 0.85 * btc_scaled + 0.15 * anchor_curve

# --- Post-2025 compression ---
post_mask = t > t0
compression = np.exp(-0.1 * (t - t0))  # exponential decay after 2025
btc_price[post_mask] *= compression[post_mask]

# Final clamp under truth arc
btc_price = np.clip(btc_price, price_min, y_derivative * 0.97)

# --- Plotting ---
fig, ax1 = plt.subplots(figsize=(12, 6))

# Red: Derivative Sigmoid
ax1.plot(t, y_derivative, color='red', linewidth=2.5, label='Truth Arc: Derivative Sigmoid')

# Blue: BTC Price (log-shaped + noise + anchors + compression)
ax1.plot(t, btc_price, color='blue', linewidth=1.8, label='BTC Price (Log-shaped, Anchored, Bounded)')

# Left Y axis
ax1.set_ylabel('BTC Price Projection (USD)', fontsize=12, color='red')
ax1.tick_params(axis='y', labelcolor='red')
ax1.set_ylim(0, peak_value * 1.1)

# Peak marker
ax1.axvline(x=t0, color='gray', linestyle=':', linewidth=1)
ax1.text(t0 + 0.5, peak_value * 0.08, 'Peak Year: 2025', color='gray')

# Orange: Sigmoid on secondary axis
ax2 = ax1.twinx()
ax2.plot(t, y_sigmoid, color='orange', linewidth=2.5, linestyle='--', label='Belief Accumulation: Sigmoid')
ax2.set_ylabel('Cumulative Belief (Arbitrary Units)', fontsize=12, color='orange')
ax2.tick_params(axis='y', labelcolor='orange')
ax2.set_ylim(0, max(y_sigmoid) * 1.05)

# Grid & Labels
plt.title('BTC Emergence: Log-shaped Price, Truth Arc & Belief Sigmoid', fontsize=14)
ax1.set_xlabel('Year', fontsize=12)
ax1.grid(True, linestyle='--', alpha=0.5)

# Unified legend
lines1, labels1 = ax1.get_legend_handles_labels()
lines2, labels2 = ax2.get_legend_handles_labels()
fig.legend(lines1 + lines2, labels1 + labels2, loc='upper left', fontsize=10)

plt.tight_layout()
plt.show()