#!/usr/bin/env python3 """ Braided Field Simulation with Genetic Event Primitives This script applies the 4 genetic event primitives (A, T, G, C) from spectral encoding to the braided field system, exploring how these perturbations affect topological states. """ import numpy as np import cmath from dataclasses import dataclass from typing import List, Tuple import matplotlib.pyplot as plt @dataclass class GeneticEvent: """A genetic event primitive (A, T, G, C).""" event_type: str # 'A', 'T', 'G', 'C' spectral_bin: int # 0, 1, 2, 3 phase_perturbation: float amplitude_perturbation: float class GeneticPrimitives: """The 4 genetic event primitives from spectral encoding.""" def __init__(self): # Map events to spectral bins and perturbations self.events = { 'A': GeneticEvent('A', 0, 0.0, 1.0), # Bin 0, no phase shift, max amplitude 'T': GeneticEvent('T', 1, np.pi/2, 1.0), # Bin 1, π/2 phase shift 'G': GeneticEvent('G', 2, np.pi, 1.0), # Bin 2, π phase shift 'C': GeneticEvent('C', 3, 3*np.pi/2, 1.0), # Bin 3, 3π/2 phase shift } def get_event(self, event_type: str) -> GeneticEvent: return self.events[event_type] def all_events(self) -> List[GeneticEvent]: return list(self.events.values()) class BraidedFieldWithGenetics: """Braided field that accepts genetic event perturbations.""" def __init__(self, num_particles: int = 4): self.particles = [] self.braiding_history = [] self.genetic_perturbations = [] self.magnetic_field = 0.0 self.spectral_bins = [0.0 + 0j] * 8 # 8 spectral bins # Initialize particles at different positions for i in range(num_particles): angle = 2 * np.pi * i / num_particles self.particles.append({ 'position': (np.cos(angle), np.sin(angle)), 'phase': 0.0, 'amplitude': 1.0 }) def apply_genetic_event(self, event: GeneticEvent): """Apply a genetic event perturbation to the braided field.""" self.genetic_perturbations.append(event) # Apply phase perturbation to all particles for p in self.particles: p['phase'] += event.phase_perturbation # Apply amplitude perturbation to spectral bin self.spectral_bins[event.spectral_bin] += event.amplitude_perturbation * cmath.exp(1j * event.phase_perturbation) # Record as a braiding operation self.braiding_history.append({ 'type': 'genetic', 'event': event.event_type, 'phase_shift': event.phase_perturbation, 'amplitude': event.amplitude_perturbation }) def apply_braiding(self, i: int, j: int, phase_shift: float): """Apply a standard braiding operation.""" if i >= len(self.particles) or j >= len(self.particles): raise IndexError("Particle index out of range") # Swap particles self.particles[i], self.particles[j] = self.particles[j], self.particles[i] # Apply phase shift self.particles[i]['phase'] += phase_shift self.particles[j]['phase'] += phase_shift # Record braiding self.braiding_history.append({ 'type': 'braid', 'i': i, 'j': j, 'phase_shift': phase_shift }) def total_wavefunction(self) -> complex: """Compute total wavefunction from all particles.""" psi = 0j for p in self.particles: psi += p['amplitude'] * cmath.exp(1j * p['phase']) return psi def spectral_signature(self) -> List[complex]: """Get the spectral signature from accumulated genetic events.""" return self.spectral_bins def topological_invariant(self) -> float: """Compute topological invariant from braiding history.""" total = 0.0 for op in self.braiding_history: if op['type'] == 'braid': total += op['phase_shift'] elif op['type'] == 'genetic': total += op['phase_shift'] return total def is_topologically_protected(self) -> bool: """Check if field is topologically protected.""" return self.topological_invariant() != 0 and self.magnetic_field > 0 def simulate_genetic_perturbations(): """Simulate applying genetic event primitives to braided field.""" print("=== Braided Field with Genetic Event Primitives ===\n") # Initialize system primitives = GeneticPrimitives() field = BraidedFieldWithGenetics(num_particles=4) print(f"Initial state:") print(f" Particles: {len(field.particles)}") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Topological invariant: {field.topological_invariant():.4f}\n") # Apply each genetic event print("Applying genetic event primitives:") for event in primitives.all_events(): field.apply_genetic_event(event) print(f" Event {event.event_type}:") print(f" Spectral bin: {event.spectral_bin}") print(f" Phase perturbation: {event.phase_perturbation:.4f} rad") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Topological invariant: {field.topological_invariant():.4f}") print() # Show spectral signature print("Spectral signature after genetic perturbations:") for i, bin_val in enumerate(field.spectral_bins[:4]): print(f" Bin {i}: {bin_val:.4f}") print() # Apply magnetic field field.magnetic_field = 1.0 print(f"Applied magnetic field: {field.magnetic_field}") print(f"Topologically protected: {field.is_topologically_protected()}\n") print(f"Final topological invariant: {field.topological_invariant():.4f}") print(f"Total operations: {len(field.braiding_history)}") def simulate_genetic_braiding_sequence(): """Simulate alternating genetic events and braiding operations.""" print("\n=== Genetic-Braiding Sequence Simulation ===\n") primitives = GeneticPrimitives() field = BraidedFieldWithGenetics(num_particles=4) sequence = [ ('genetic', 'A'), ('braid', (0, 1, np.pi/4)), ('genetic', 'T'), ('braid', (1, 2, np.pi/3)), ('genetic', 'G'), ('braid', (2, 3, np.pi/5)), ('genetic', 'C'), ('braid', (0, 3, np.pi/2)), ] print(f"Initial wavefunction: {field.total_wavefunction():.4f}") print(f"Initial invariant: {field.topological_invariant():.4f}\n") for op_type, data in sequence: if op_type == 'genetic': event = primitives.get_event(data) field.apply_genetic_event(event) print(f"Genetic event {data}:") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Invariant: {field.topological_invariant():.4f}") elif op_type == 'braid': i, j, phase = data field.apply_braiding(i, j, phase) print(f"Braid ({i},{j}) with phase {phase:.4f}:") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Invariant: {field.topological_invariant():.4f}") print() field.magnetic_field = 1.0 print(f"Applied magnetic field: {field.magnetic_field}") print(f"Topologically protected: {field.is_topologically_protected()}") print(f"Final invariant: {field.topological_invariant():.4f}") def plot_genetic_phase_space(): """Visualize genetic event perturbations in phase space.""" print("\n=== Genetic Event Phase Space ===\n") primitives = GeneticPrimitives() # Get phase shifts for each event events = primitives.all_events() phases = [e.phase_perturbation for e in events] amplitudes = [e.amplitude_perturbation for e in events] labels = [e.event_type for e in events] bins = [e.spectral_bin for e in events] # Create polar plot fig, ax = plt.subplots(figsize=(8, 8), subplot_kw=dict(projection='polar')) # Plot each event as a point for phase, amp, label, bin_idx in zip(phases, amplitudes, labels, bins): ax.plot(phase, amp, 'o', markersize=12, label=f'{label} (bin {bin_idx})') ax.annotate(label, (phase, amp), xytext=(10, 10), textcoords='offset points', fontsize=10) # Draw lines from origin for phase, amp in zip(phases, amplitudes): ax.plot([0, phase], [0, amp], 'b-', alpha=0.3) ax.set_title('Genetic Event Primitives in Phase Space', pad=20) ax.set_xlabel('Phase (radians)') ax.set_ylabel('Amplitude') ax.grid(True, alpha=0.3) ax.legend(loc='upper right') plt.tight_layout() plt.savefig('/tmp/genetic_phase_space.png', dpi=150) print("Genetic phase space plot saved to /tmp/genetic_phase_space.png") def simulate_genetic_topological_encoding(): """Simulate encoding information in braided field using genetic events.""" print("\n=== Topological Encoding with Genetic Events ===\n") primitives = GeneticPrimitives() field = BraidedFieldWithGenetics(num_particles=4) # Encode "ATGC" sequence sequence = ['A', 'T', 'G', 'C'] print(f"Encoding sequence: {''.join(sequence)}") print(f"Initial wavefunction: {field.total_wavefunction():.4f}") print(f"Initial invariant: {field.topological_invariant():.4f}\n") for event_type in sequence: event = primitives.get_event(event_type) field.apply_genetic_event(event) print(f"Encoded {event_type}:") print(f" Wavefunction: {field.total_wavefunction():.4f}") print(f" Invariant: {field.topological_invariant():.4f}") # Apply magnetic field to lock topology field.magnetic_field = 1.0 print(f"\nApplied magnetic field: {field.magnetic_field}") print(f"Topologically protected: {field.is_topologically_protected()}") # Check if information is preserved in topology final_invariant = field.topological_invariant() print(f"\nFinal topological invariant: {final_invariant:.4f}") # The invariant encodes the sequence information expected_invariant = sum(e.phase_perturbation for e in primitives.all_events()) print(f"Expected invariant (sum of phases): {expected_invariant:.4f}") print(f"Match: {abs(final_invariant - expected_invariant) < 1e-10}") print("\nThe genetic sequence is now encoded in the topological invariant,") print("making it immune to local perturbations.") if __name__ == "__main__": simulate_genetic_perturbations() simulate_genetic_braiding_sequence() plot_genetic_phase_space() simulate_genetic_topological_encoding() print("\n=== Simulation Complete ===") print("Genetic event primitives (A, T, G, C) successfully applied to braided field.") print("The 4 primitives create distinct phase perturbations that affect") print("the topological invariant, enabling information encoding in") print("the braided field topology.")