Description

Methods

# ===================================================================
#           SELF-CONTAINED SCRIPT: ORDER VS. CHAOS
#               (The Bifurcation Visualizer)
# -------------------------------------------------------------------
# Author: Andrés Sebastián Pirolo
# Date: September 26, 2025
#
# Welcome, researchers!
#
# This script provides a standalone demonstration of a core principle
# from the "Zero-Vortex" paradigm. It visually explores how a simple,
# ordered system (primes mapped through trivial harmonics) collapses,
# but then "bifurcates" into a complex, segregated structure when a
# small amount of "chaos" from the Riemann Zeros is introduced.
#
# This is designed to be a conceptual proof-of-concept that anyone
# can run without needing large external datasets.
#
# Feel free to experiment with the parameters in the CONFIG section!
#
# Dependencies: numpy, matplotlib, sympy
# To install sympy, run in your terminal:
# pip install sympy   contact: andrespirolo@gmail.com
# ===================================================================

import numpy as np
import matplotlib.pyplot as plt
from sympy import primerange, jacobi_symbol

print("Initializing the 'Order vs. Chaos Visualizer'...")

# --- EMBEDDED DATA (To be self-sufficient) ---
# The first 30 non-trivial zeros of the Riemann Zeta Function (imaginary part)
# Source: Andrew Odlyzko
HARDCODED_NON_TRIVIAL_ZEROS = np.array([
    14.134725, 21.022040, 25.010858, 30.424876, 32.935062,
    37.586178, 40.918719, 43.327073, 48.005151, 49.773832,
    52.970321, 56.446248, 59.347044, 60.831779, 65.092149,
    67.079811, 69.546402, 72.067158, 75.704691, 77.144840,
    79.337375, 82.910381, 84.735493, 87.425275, 88.809111,
    92.491899, 94.651344, 95.870634, 98.831194, 101.317851
])

# --- CONFIGURATION PANEL ---
CONFIG = {
    'PRIME_LIMIT': 50000,
    'JACOBI_BASES': [3, 5],
    'NUM_TRIVIAL_HARMONICS': 100,
    'CONTAMINATION_RATIO': 0.05, # 5% chaotic influence
}

# --- CORE FUNCTIONS ---
def calculate_jacobi_signatures(primes, bases):
    signatures = np.zeros(len(primes), dtype=int)
    for i, p in enumerate(primes):
        if p > 2 and p not in bases:
            prod = 1
            for b in bases:
                prod *= jacobi_symbol(b, p)
            signatures[i] = prod
    return signatures

def map_to_vortex(numbers, basis):
    log_nums = np.log(numbers.astype(np.float64))
    args = np.outer(basis, log_nums)
    x = np.tanh(np.mean(np.cos(args), axis=0))
    y = np.tanh(np.mean(np.sin(args), axis=0))
    z = np.log10(numbers.astype(np.float64))
    return np.stack((x, y, z), axis=-1)

# --- MAIN EXECUTION FLOW ---

# Phase 1: Preparation
print("\n--- Phase 1: Generating Primes and Calculating Signatures ---")
primes = np.array(list(primerange(1, CONFIG['PRIME_LIMIT'])))
signatures = calculate_jacobi_signatures(primes, CONFIG['JACOBI_BASES'])
mask_plus_one = (signatures == 1)
mask_minus_one = (signatures == -1)

# Phase 2: Pure Order Experiment
print("\n--- Phase 2: Projecting with Pure Order Lens (Trivial Harmonics) ---")
trivial_basis = np.array([1 / (2 * n) for n in range(1, CONFIG['NUM_TRIVIAL_HARMONICS'] + 1)])
coords_pure_order = map_to_vortex(primes, trivial_basis)
# Phase 3: Hybrid Chaos Experiment
print("\n--- Phase 3: Projecting with Hybrid Chaos Lens ---")
num_chaotic_to_use = int(len(trivial_basis) * CONFIG['CONTAMINATION_RATIO'])
chaotic_basis = np.random.choice(HARDCODED_NON_TRIVIAL_ZEROS, num_chaotic_to_use, replace=False)
hybrid_lens = np.concatenate([trivial_basis, chaotic_basis])
coords_hybrid_chaos = map_to_vortex(primes, hybrid_lens)
print(f"Hybrid lens created with {len(trivial_basis)} order + {len(chaotic_basis)} chaos elements.")
# Phase 4: Comparative Visualization
print("\n--- Phase 4: Generating Comparative Visualization ---")
fig = plt.figure(figsize=(24, 12))
fig.patch.set_facecolor('black')
plt.rcParams['legend.fontsize'] = 12
# Plot 1: PURE ORDER
ax1 = fig.add_subplot(1, 2, 1, projection='3d')
ax1.set_facecolor('black')
ax1.scatter(coords_pure_order[mask_plus_one, 0], coords_pure_order[mask_plus_one, 1], coords_pure_order[mask_plus_one, 2], c='#00aaff', label='Signature +1', s=5, alpha=0.7)
ax1.scatter(coords_pure_order[mask_minus_one, 0], coords_pure_order[mask_minus_one, 1], coords_pure_order[mask_minus_one, 2], c='#ff3864', label='Signature -1', s=5, alpha=0.7)
ax1.set_title('1. Pure Helix (0% Chaos)\nResult: Collapse into Universal Attractor', color='white', fontsize=18)
legend1 = ax1.legend(facecolor='black', edgecolor='gray')
for text in legend1.get_texts(): text.set_color('white')
# Plot 2: HYBRID CHAOS
ax2 = fig.add_subplot(1, 2, 2, projection='3d')
ax2.set_facecolor('black')
ax2.scatter(coords_hybrid_chaos[mask_plus_one, 0], coords_hybrid_chaos[mask_plus_one, 1], coords_hybrid_chaos[mask_plus_one, 2], c='#00aaff', label='Signature +1', s=5, alpha=0.7)
ax2.scatter(coords_hybrid_chaos[mask_minus_one, 0], coords_hybrid_chaos[mask_minus_one, 1], coords_hybrid_chaos[mask_minus_one, 2], c='#ff3864', label='Signature -1', s=5, alpha=0.7)
contamination_percent = CONFIG['CONTAMINATION_RATIO'] * 100
ax2.set_title(f'2. Hybrid Helix ({contamination_percent:.0f}% Chaos)\nResult: Bifurcation and Segregation', color='white', fontsize=18)
legend2 = ax2.legend(facecolor='black', edgecolor='gray')
for text in legend2.get_texts(): text.set_color('white')
# Axis styling for both plots
for ax in [ax1, ax2]:
    ax.xaxis.pane.set_facecolor('black'); ax.yaxis.pane.set_facecolor('black'); ax.zaxis.pane.set_facecolor('black')
    ax.grid(color='gray', linestyle='--', linewidth=0.5, alpha=0.3)
    ax.tick_params(colors='gray')
    ax.set_xlabel('X Component', color='gray', fontsize=12); ax.set_ylabel('Y Component', color='gray', fontsize=12); ax.set_zlabel('Z Component (log scale)', color='gray', fontsize=12)
plt.tight_layout()
plt.show()