1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
|
#!/usr/bin/env python3
import numpy as np
import matplotlib.pyplot as plt
from alive_progress import alive_bar
img_res_x = 250
img_res_y = 250
total_pixels = img_res_x * img_res_y # so we don't gotta compute it every time
periods = 1
square_x = 0
square_y = 0
xmin = (-periods * np.pi) + (square_x * np.pi)
xmax = (periods * np.pi) + (square_x * np.pi)
ymin = (-periods * np.pi) + (square_y * np.pi)
ymax = (periods * np.pi) + (square_y * np.pi)
#xmin = -10
#xmax = 10
#ymin = -10
#ymax = 10
escape = 10000
iterations = 255*3
c_x = 2 * np.pi
c_y = 2 * np.pi
grid = np.meshgrid(np.linspace(ymin, ymax, 200), np.linspace(xmin, xmax, 200))
#image = np.meshgrid(np.linspace(ymin, ymax, img_res_y), np.linspace(xmin, xmax, img_res_x))
image = np.zeros([img_res_y, img_res_x], dtype=np.double)
class point_charge():
def __init__(self, x, y, c, mod):
self.x = x
self.y = y
self.c = c
self.mod = mod
def get_field(self, to_x, to_y):
if(self.mod):
to_x = (to_x % self.mod)
to_y = (to_y % self.mod)
return np.array([
((self.c * (self.x - to_x)) / ((self.x - to_x)**2 + (self.y - to_y)**2)**1.5),
((self.c * (self.y - to_y)) / ((self.x - to_x)**2 + (self.y - to_y)**2)**1.5)])
#will remove all the point charge code if it turns out to be good enough to be impliemnted into openCL
#point_charges = [point_charge(-5, -5, 100), point_charge(-5, 5, -100), point_charge(5, 0, 100)]
#point_charges = [point_charge(-1,-1, 100, 10), point_charge(1,1,-100, 0)]
point_charges = []
#plt.ion()
ax = plt.gca()
fig = plt.gcf()
#ax.set_autoscale_on(False)
#ax.set_xlim([xmin, xmax])
#ax.set_ylim([ymin, ymax])
vector_arrows = None
def show_field():
global vector_arrows
grid_f = np.zeros_like(grid)
for p in point_charges:
grid_f += p.get_field(grid[0], grid[1])
#plt.streamplot(grid[0], grid[1], grid_f[0], grid_f[1], density=5)
vector_arrows = plt.quiver(grid[0], grid[1], grid_f[0], grid_f[1])
plt.show(block=False)
plt.pause(.1)
#show_field()
timestep = .1
def test_sim():
particle_grid = np.meshgrid(np.linspace(ymin, ymax, 100), np.linspace(xmin, xmax, 100))
pos = particle_grid
acceleration = np.zeros_like(particle_grid)
velocity = np.zeros_like(particle_grid)
velocity = [np.ones_like(particle_grid[0]) * 1, np.ones_like(particle_grid[0]) * .5]
mass = 10
charge = 1
particle_plot = ax.plot(velocity[0], velocity[1], 'bo', animated=True)
#velocity += .1
background = fig.canvas.copy_from_bbox(ax.bbox)
ax.draw_artist(vector_arrows)
fig.canvas.blit(fig.bbox)
while True:
fig.canvas.restore_region(background)
field = np.zeros_like(particle_grid)
# TODO can make this quicker by skipping initilization
for p in point_charges:
field += p.get_field(pos[0], pos[1])
acceleration = ((charge * field) / mass) * timestep
#print(acceleration)
velocity += acceleration * timestep
pos += velocity * timestep
fig.canvas.restore_region(background)
particle_plot[0].set_data(pos[0],pos[1])
ax.draw_artist(particle_plot[0])
fig.canvas.blit(fig.bbox)
fig.canvas.flush_events()
plt.pause(1/60)
#fig.canvas.draw_idle()
#test_sim()
#exit(1)
max_timesteps = 10
def get_fractal_iter(img):
next_x = img[1][y][x] / np.sin(img[0][y][x])
img[0][y][x] = img[0][y][x] / np.sin(img[1][y][x])
img[1][y][x] = next_x
if (np.square(img[0][y][x]) + np.square(img[1][y][x])) >= escape:
z[y][x] = i
#meshgrid makes things slower as we can't test individual points for breaking to infinity;
#however, I will fix that later.
cmap = plt.cm.viridis
cmap.set_bad((0,0,0))
cmap.set_over((0,0,0))
cmap.set_under((0,0,0))
with alive_bar(img_res_y, bar = 'filling', spinner = 'waves') as bar:
for pix_y, y in enumerate(np.linspace(ymin, ymax, img_res_y)):
for pix_x, x in enumerate(np.linspace(xmin, xmax, img_res_x)):
on_x = x
on_y = y
for i in range(iterations):
completed_ratio = (((pix_x * pix_y * 1)) / total_pixels)
next_x = on_x/np.sin(on_y)
on_y = on_y/np.sin(on_x)
on_x = next_x
# do physics here - we could just use vectors but i keep rewriting things
timesteps = max_
acceleration = np.array([0, 0], dtype=np.double)
velocity = np.array([on_x, on_y], dtype=np.double) # maybe multiply by stuff
pos = np.array([0,0], dtype=np.double)
for t in range(timesteps):
for p in point_charges:
acceleration += p.get_field(on_x, on_y)
velocity += acceleration
pos += velocity * (timesteps)
on_x += pos[0]
on_y += pos[1]
if on_x**2 + on_y**2 > escape:
image[pix_x][pix_y] = i
break
bar()
ax.imshow(image, norm="log", aspect="auto", cmap=cmap)
plt.show()
# yeah, I shouldn't have switched to a meshgrid, oh well
#z = np.empty_like(image[0])
exit(0)
with alive_bar(img_res_x, bar = 'filling', spinner = 'waves') as bar:
for y in range(img_res_y):
for x in range(img_res_x):
for i in range(iterations):
if image[0][y][x] == np.NAN:
continue
next_x = image[1][y][x] / np.sin(image[0][y][x])
image[0][y][x] = image[0][y][x] / np.sin(image[1][y][x])
image[1][y][x] = next_x
if (np.square(image[0][y][x]) + np.square(image[1][y][x])) >= escape:
z[y][x] = i
image[0][y][x] = np.NAN
image[1][y][x] = np.NAN
break
# #do physics here
bar()
#image = np.clip(image, -escape, escape)
|
