# random_cantor_dust#

This generates a fractal image by iteratively and randomaly removing segments at successively large scales.

[1]:

import porespy as ps
import matplotlib.pyplot as plt
import numpy as np
import inspect
inspect.signature(ps.generators.random_cantor_dust)

[1]:

<Signature (shape, n, p=2, f=0.8)>


## shape#

The shape of the image can either be 2D or 3D:

[2]:

fig, ax = plt.subplots(1, 1, figsize=[6, 6])

im = ps.generators.random_cantor_dust(shape=[500, 500], n=8)
ax.imshow(im, interpolation='none')
ax.axis(False);


## n#

The number of scales to bisect the image, with higher numbers leading to large features. The algorithm starts by dividing a p x p region and randomly setting some quadrants to False. It proceeds by increasing the region size and repeating. n controls the number of iterations at larger scales.

[3]:

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

n=4
im = ps.generators.random_cantor_dust(shape=[500, 500], n=n)
ax[0].imshow(im, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'n = {n}')

n=8
im = ps.generators.random_cantor_dust(shape=[500, 500], n=n)
ax[1].imshow(im, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'n = {n}');


## f#

The probability that a quadrant survives the process (i.e. set to True)

[4]:

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

f=0.7
im = ps.generators.random_cantor_dust(shape=[500, 500], n=n, f=f)
ax[0].imshow(im, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'f = {f}')

f=0.9
im = ps.generators.random_cantor_dust(shape=[500, 500], n=n, f=f)
ax[1].imshow(im, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'f = {f}');


## p#

The size of the initial region, which is scaled by a factor of p on each step

[5]:

fig, ax = plt.subplots(1, 2, figsize=[12, 6])

p=2
im = ps.generators.random_cantor_dust(shape=[500, 500], n=8, p=p)
ax[0].imshow(im, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'p = {p}')

p=3
im = ps.generators.random_cantor_dust(shape=[500, 500], n=8, p=p)
ax[1].imshow(im, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'p = {p}');