f5f1551964
Lucidia Math - Advanced mathematical engines: forge/ - Mathematical Foundations: - consciousness.py (650 lines) - Consciousness modeling - unified_geometry.py (402 lines) - Geometric transformations - advanced_tools.py (356 lines) - Advanced utilities - main.py (209 lines) - CLI orchestration - numbers.py, proofs.py, fractals.py, dimensions.py lab/ - Experimental Mathematics: - unified_geometry_engine.py (492 lines) - Geometry engine - amundson_equations.py (284 lines) - Custom equations - iterative_math_build.py (198 lines) - Iterative construction - trinary_logic.py (111 lines) - Three-valued logic - prime_explorer.py (108 lines) - Prime exploration - quantum_finance.py (83 lines) - Quantum finance models 3,664 lines of Python. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <noreply@anthropic.com>
109 lines
3.2 KiB
Python
109 lines
3.2 KiB
Python
"""Prime pattern exploration and visualization utilities."""
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from __future__ import annotations
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from dataclasses import dataclass
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from pathlib import Path
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from typing import Tuple
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import matplotlib.pyplot as plt
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import numpy as np
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import sympy as sp
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from .frameworks import select_backend
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@dataclass
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class PrimeVisualizer:
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output_dir: Path
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def save_fig(self, fig: plt.Figure, name: str) -> None:
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self.output_dir.mkdir(parents=True, exist_ok=True)
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png = self.output_dir / f"{name}.png"
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svg = self.output_dir / f"{name}.svg"
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fig.savefig(png)
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fig.savefig(svg)
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plt.close(fig)
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def ulam_spiral(size: int, *, backend: str | None = None) -> Tuple[np.ndarray, np.ndarray]:
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"""Generate an Ulam spiral and mask of prime numbers."""
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if backend is not None and backend != "numpy":
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# Prime detection relies on SymPy; use numpy for now but validate name.
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select_backend(backend)
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grid = np.zeros((size, size), dtype=int)
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x = y = size // 2
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dx, dy = 0, -1
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for n in range(1, size * size + 1):
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if -size // 2 <= x < size // 2 and -size // 2 <= y < size // 2:
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grid[y + size // 2, x + size // 2] = n
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if x == y or (x < 0 and x == -y) or (x > 0 and x == 1 - y):
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dx, dy = -dy, dx
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x, y = x + dx, y + dy
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prime_mask = np.vectorize(sp.isprime)(grid).astype(bool)
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return grid, prime_mask
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def plot_ulam(grid: np.ndarray, mask: np.ndarray) -> plt.Figure:
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fig, ax = plt.subplots()
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ax.imshow(mask, cmap="Greys")
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ax.set_xticks([])
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ax.set_yticks([])
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return fig
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def residue_grid(mod: int, size: int = 100, *, backend: str | None = None) -> np.ndarray:
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"""Compute a modular residue grid.
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Parameters
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----------
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mod:
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The modulus used for the residue computation.
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size:
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Total number of integers to include. ``size`` must be a perfect
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square so that the numbers can be reshaped into a square grid.
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Raises
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------
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ValueError
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If ``size`` is not a perfect square.
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"""
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backend_cfg = select_backend(backend)
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xp = backend_cfg.array_module
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numbers = xp.arange(1, size + 1)
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side = int(np.sqrt(size))
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if side * side != size:
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raise ValueError("size must be a perfect square")
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grid = xp.reshape(numbers, (side, side)) % mod
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return np.asarray(grid)
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def plot_residue(grid: np.ndarray) -> plt.Figure:
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fig, ax = plt.subplots()
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ax.imshow(grid, cmap="viridis")
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ax.set_xticks([])
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ax.set_yticks([])
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return fig
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def fourier_prime_gaps(limit: int, *, backend: str | None = None) -> Tuple[np.ndarray, np.ndarray]:
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"""Return prime gaps and their Fourier transform magnitude."""
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primes = list(sp.primerange(2, limit))
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backend_cfg = select_backend(backend)
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xp = backend_cfg.array_module
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gaps = xp.diff(xp.asarray(primes, dtype=float))
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fft = xp.abs(xp.fft.fft(gaps))
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return np.asarray(gaps, dtype=float), np.asarray(fft, dtype=float)
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def plot_fourier(gaps: np.ndarray, fft: np.ndarray) -> plt.Figure:
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fig, ax = plt.subplots(2, 1, figsize=(6, 6))
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ax[0].plot(gaps)
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ax[0].set_title("Prime gaps")
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ax[1].plot(fft)
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ax[1].set_title("FFT magnitude")
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return fig
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