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December 22, 2018 22:32
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Julia set plotting example (5k res, so kinda slow)
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""" | |
Copyright (C) 2018 Torin Cooper-Bennun | |
This program is free software: you can redistribute it and/or modify | |
it under the terms of the GNU General Public License as published by | |
the Free Software Foundation, either version 3 of the License, or | |
(at your option) any later version. | |
This program is distributed in the hope that it will be useful, | |
but WITHOUT ANY WARRANTY; without even the implied warranty of | |
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
GNU General Public License for more details. | |
You should have received a copy of the GNU General Public License | |
along with this program. If not, see <https://www.gnu.org/licenses/>. | |
simple Julia set plotting | |
""" | |
import numpy as np | |
import matplotlib.pyplot as plt | |
import matplotlib.cm as cm | |
def iterate_quad_poly(z_0, c, n_max): | |
""" | |
iterates | |
z_{k+1} = z_k^2 + c | |
while |z_k| < 2, returning the value of k (k_esc) if this condition is breached; iterates a maximum of *n_max* | |
times, such that 0 < k_esc <= *n_max*. | |
initial parameters *z_0* and *c* are complex numbers. | |
""" | |
z = z_0 | |
for k in range(n_max): | |
if abs(z) >= 2: | |
return k | |
z = z*z + c | |
return n_max | |
def julia_calc(c=0.1+0.12j, z_bottomleft=-2.5-2.5j, z_topright=2.5+2.5j, img_width=600): | |
aspect = (z_topright - z_bottomleft).real / (z_topright - z_bottomleft).imag | |
img_height = int(img_width / aspect) | |
escape_times = np.zeros((img_height, img_width)) | |
n_max = 100 | |
for i_r, R in enumerate(np.linspace(z_bottomleft.real, z_topright.real, img_width)): | |
for i_i, I in enumerate(np.linspace(z_bottomleft.imag, z_topright.imag, img_height)): | |
print(f"{(i_i + i_r*img_height)/(img_width*img_height)*100:.2f}% complete ", end="\r") | |
escape_times[i_i, i_r] = iterate_quad_poly(R + I*1j, c, n_max) | |
print() | |
return escape_times | |
def julia_plot(escape_times, n_max, fname=None): | |
img_height, img_width = escape_times.shape | |
dpi = 100 | |
fig, ax = plt.subplots(figsize=(img_width/dpi, img_height/dpi), dpi=dpi) | |
ax.tick_params(which="both", left=False, bottom=False, labelleft=False, labelbottom=False) | |
ax.set_aspect(1) | |
cmap = cm.get_cmap("seismic") | |
cmap.set_over("k") | |
print("Plotting...") | |
ax.imshow(escape_times, cmap=cmap, vmax=n_max-1) | |
ax.set_position([0, 0, 1, 1]) | |
if fname: | |
print("Saving...") | |
fig.savefig(fname) | |
if __name__ == "__main__": | |
aspect = 1920/1080 | |
height = 2.4 | |
width = height*aspect | |
z_bl = -width/2 - height/2 *1j | |
z_tr = -z_bl | |
print("Generating data...") | |
data = julia_calc(c=-0.74543+0.11301j, z_bottomleft=z_bl, z_topright=z_tr, img_width=5120) | |
np.savetxt("julia_test_big.txt", data) | |
julia_plot(data, 100, "julia_5k.png") |
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