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https://github.com/blackboxprogramming/BlackRoad-Operating-System.git
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0108860bff
Create comprehensive research-lab pack structure with mathematical and quantum computing modules from blackroad-prism-console: Math Modules: - hilbert_core.py: Hilbert space symbolic reasoning - collatz/: Distributed Collatz conjecture verification - linmath/: Linear mathematics C library - lucidia_math_forge/: Symbolic proof engine - lucidia_math_lab/: Experimental mathematics Quantum Modules: - lucidia_quantum/: Quantum core - quantum_engine/: Circuit simulation Experiments: - br_math/: Gödel gap, quantum experiments Includes pack.yaml manifest and comprehensive README. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <noreply@anthropic.com>
52 lines
1.4 KiB
Python
52 lines
1.4 KiB
Python
"""Fractal generators for the Lucidia Math Forge.
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The :func:`generate_fractal` function accepts a recursion rule and writes
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a simple fractal image to disk. Rules operate on complex numbers and
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are intentionally simple to keep execution fast in constrained
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environments.
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"""
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from __future__ import annotations
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from typing import Callable
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import matplotlib.pyplot as plt
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import numpy as np
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def julia_rule(z: complex, c: complex) -> complex:
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"""Default Julia set rule ``z^2 + c``."""
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return z * z + c
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def generate_fractal(
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rule: Callable[[complex, complex], complex] = julia_rule,
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filename: str = "fractal.png",
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iterations: int = 50,
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bounds=(-2.0, 2.0, -2.0, 2.0),
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resolution: int = 300,
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) -> str:
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"""Generate a fractal image using ``rule`` and save it to ``filename``."""
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xmin, xmax, ymin, ymax = bounds
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x = np.linspace(xmin, xmax, resolution)
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y = np.linspace(ymin, ymax, resolution)
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c = x[:, None] + 1j * y[None, :]
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z = np.zeros_like(c)
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mask = np.ones(c.shape, dtype=bool)
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for _ in range(iterations):
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z[mask] = rule(z[mask], c[mask])
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mask &= np.abs(z) < 2
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plt.imshow(mask.T, extent=bounds, cmap="magma")
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plt.axis("off")
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plt.savefig(filename, bbox_inches="tight", pad_inches=0)
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plt.close()
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return filename
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if __name__ == "__main__":
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# Create a quick Julia set image.
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print("Saved fractal to", generate_fractal())
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