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Ingy döt Net 2025-06-11 20:16:52 -04:00
parent 72eb4943cb
commit 4d5544505c
2347 changed files with 62432 additions and 16731 deletions
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50
Task/Mandelbrot-set/Python/mandelbrot-set-8.py
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@ -1,10 +1,11 @@
import numpy as np
import numba as nb
import matplotlib.pyplot as plt
import decimal as dc # decimal floating point arithmetic with arbitrary precision
dc.getcontext().prec = 80 # set precision to 80 digits (about 256 bits)
d, h = 50, 1000 # pixel density (= image width) and image height
d, h = 100, 2000 # pixel density (= image width) and image height
n, r = 80000, 100000 # number of iterations and escape radius (r > 2)
a = dc.Decimal("-1.256827152259138864846434197797294538253477389787308085590211144291")
@ -15,8 +16,8 @@ u, v = dc.Decimal(0), dc.Decimal(0)
for k in range(n+1):
S[k] = float(u) + float(v) * 1j
if u ** 2 + v ** 2 < r ** 2:
u, v = u ** 2 - v ** 2 + a, 2 * u * v + b
if u * u + v * v < r * r:
u, v = u * u - v * v + a, 2 * u * v + b
else:
print("The reference sequence diverges within %s iterations." % k)
break
@ -25,20 +26,43 @@ x = np.linspace(0, 2, num=d+1, dtype=np.float64)
y = np.linspace(0, 2 * h / d, num=h+1, dtype=np.float64)
A, B = np.meshgrid(x * np.pi, y * np.pi)
C = 8.0 * np.exp((A + B * 1j) * 1j)
C = (- 8.0) * np.exp((A + B * 1j) * 1j)
E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
D, I, J = np.zeros(C.shape), np.zeros(C.shape, dtype=np.int64), np.zeros(C.shape, dtype=np.int64)
@nb.njit(parallel=True)
def calculation(C):
E, I = np.zeros_like(C), np.zeros(C.shape, dtype=np.int64)
Z, dZ = np.zeros_like(C), np.zeros_like(C)
for k in range(n):
Z2 = Z.real ** 2 + Z.imag ** 2
M, R = Z2 < r ** 2, Z2 < E.real ** 2 + E.imag ** 2
E[R], I[R] = Z[R], J[R] # rebase when z is closer to zero
E[M], I[M] = (2 * S[I[M]] + E[M]) * E[M] + C[M], I[M] + 1
Z[M], dZ[M] = S[I[M]] + E[M], 2 * Z[M] * dZ[M] + 1
def iteration(C):
E, I = np.zeros_like(C), np.zeros(C.shape, dtype=np.int64)
Z, dZ = np.zeros_like(C), np.zeros_like(C)
def abs2(z):
return z.real * z.real + z.imag * z.imag
def iterate(E, I, Z, dZ, C):
E, I = (2 * S[I] + E) * E + C, I + 1
Z, dZ = S[I] + E, 2 * Z * dZ + 1
return E, I, Z, dZ
for k in range(n):
M = abs2(Z) < abs2(E)
E[M], I[M] = Z[M], 0 # rebase when z is closer to zero
M = abs2(Z) < abs2(r)
E[M], I[M], Z[M], dZ[M] = iterate(E[M], I[M], Z[M], dZ[M], C[M])
return E, I, Z, dZ
for j in nb.prange(C.shape[1]):
E[:,j], I[:,j], Z[:,j], dZ[:,j] = iteration(C[:,j])
return E, I, Z, dZ
E, I, Z, dZ = calculation(C)
D = np.zeros(C.shape, dtype=np.float64)
N = abs(Z) > 2 # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])
plt.imshow(D.T ** 0.015, cmap=plt.cm.nipy_spectral, origin="lower")
plt.imshow(D.T ** 0.015, cmap=plt.cm.gist_ncar, origin="lower")
plt.savefig("Mercator_Mandelbrot_deep_map.png", dpi=200)