Mandelbrot set: Difference between revisions

Line 7,230:

plt.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted)

plt.savefig("~~Mandelbrot_escape_time~~.png", dpi=250)

plt.savefig("Mandelbrot_set_1.png", dpi=250)

N = abs(Z) > r

N = abs(Z) > r # normalized iteration count

T[N] = T[N] - np.log2(np.log(abs(Z[N])) / np.log(r))

plt.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted)

plt.savefig("~~Mandelbrot_normalized_count~~.png", dpi=250)

plt.savefig("Mandelbrot_set_2.png", dpi=250)

N = abs(Z) > 2

N = abs(Z) > 2 # exterior distance estimation

D[N] = 0.5 * np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

plt.imshow(D ** 0.1, cmap=plt.cm.twilight_shifted)

plt.savefig("~~Mandelbrot_distance_estimation~~.png", dpi=250)

plt.savefig("Mandelbrot_set_3.png", dpi=250)

X, Y = C.real, C.imag

S = 150 * 2 / d # scaling depends on ~~the size of the figure~~

S = 150 * 2 / d # scaling depends on figsize

fig, ax = plt.subplots(figsize=(8, 6))

ax.scatter(X, Y, s=S**2, c=D**0.1, cmap=plt.cm.twilight_shifted)

plt.savefig("~~Mandelbrot_scatter_plot~~.png", dpi=250)</lang>

plt.savefig("Mandelbrot_plot.png", dpi=250)</lang>

A small change in the above code allows Mercator maps of the Mandelbrot set (see David Madore: [http://www.madore.org/~david/math/mandelbrot.html ''Mandelbrot set images and videos''] and Anders Sandberg: [https://www.flickr.com/photos/arenamontanus/sets/72157615740829949 ''Mercator Mandelbrot Maps'']).

The maximum magnification is exp(2*pi*h/d) = exp(2*pi*5.5) = 535.5^5.5 = 10^15, which is also the maximum for 64-bit arithmetic.

Line 7,268:

Z, dZ = np.zeros_like(C), np.zeros_like(C)

D = np.zeros(C.shape)

T, D = np.zeros(C.shape), np.zeros(C.shape)

for k in range(n):

M = abs(Z) < r

Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1

T[M] = T[M] + 1

plt.imshow(T.T ** 0.1, cmap=plt.cm.nipy_spectral_r)

N = abs(Z) > 2

plt.savefig("Mercator_map_1.png", dpi=250)

N = abs(Z) > r # normalized iteration count

T[N] = T[N] - np.log2(np.log(abs(Z[N])) / np.log(r))

plt.imshow(T.T ** 0.1, cmap=plt.cm.nipy_spectral_r)

plt.savefig("Mercator_map_2.png", dpi=250)

N = abs(Z) > 2 # exterior distance estimation

D[N] = 0.5 * np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

plt.imshow(D.T ** 0.1, cmap=plt.cm.nipy_spectral)

plt.savefig("~~Mandelbrot_Mercator_map~~.png", dpi=250)

plt.savefig("Mercator_map_3.png", dpi=250)

X, Y = C.real, C.imag

S = 150 * 2 / d * np.pi * np.exp(-B) # scaling depends on ~~the size of the figure~~

S = 150 * 2 / d * np.pi * np.exp(-B) # scaling depends on figsize

fig, ax = plt.subplots(2, 2, figsize=(16, 16))

Line 7,288:

Line 7,298:

ax[1, 0].scatter(X[200:500], Y[200:500], s=S[0:300]**2, c=D[200:500]**0.3, cmap=plt.cm.nipy_spectral)

ax[1, 1].scatter(X[300:600], Y[300:600], s=S[0:300]**2, c=D[300:600]**0.2, cmap=plt.cm.nipy_spectral)

plt.savefig("~~Mandelbrot_Mercator_zoom~~.png", dpi=250)</lang>

plt.savefig("Mandelbrot_zoom.png", dpi=250)</lang>

=={{header|R}}==