import logging
import numpy as np
import scipy.ndimage as spim
from porespy.tools import get_tqdm
from porespy import settings
tqdm = get_tqdm()
logger = logging.getLogger(__name__)
__all__ = [
'random_cantor_dust',
'sierpinski_foam',
'sierpinski_foam2',
]
[docs]
def random_cantor_dust(shape, n: int = 5, p: int = 2, f: float = 0.8, seed: int = None):
r"""
Generates an image of random cantor dust
Parameters
----------
shape : array_like
The shape of the final image. If not evenly divisible by $p**n$
it will be increased to the nearest size that is.
n : int
The number of times to iteratively divide the image.
p : int (default = 2)
The number of divisions to make on each iteration.
f : float (default = 0.8)
The fraction of the set to keep on each iteration.
seed : int, optional, default = `None`
Initializes numpy's random number generator to the specified state. If not
provided, the current global value is used. This means calls to
``np.random.state(seed)`` prior to calling this function will be respected.
Returns
-------
dust : ndarray
A boolean image of a random Cantor dust
Examples
--------
`Click here
<https://porespy.org/examples/generators/reference/randon_cantor_dust.html>`_
to view online example.
"""
if seed is not None:
np.random.seed(seed)
# Parse the given shape and adjust if necessary
shape = np.array(shape)
trim = np.mod(shape, (p**n))
if np.any(trim > 0):
shape = shape - trim + p**n
logger.warning(f"Requested shape being changed to {shape}")
im = np.ones(shape, dtype=bool)
divs = []
if isinstance(n, int):
for i in range(1, n):
divs.append(p**i)
else:
for i in n:
divs.append(p**i)
for i in tqdm(divs, **settings.tqdm):
sh = (np.array(im.shape)/i).astype(int)
mask = np.random.rand(*sh) < f
mask = spim.zoom(mask, zoom=i, order=0)
im = im*mask
return im
def sierpinski_foam2(shape, n: int = 5):
r"""
Generates an image of a Sierpinski carpet or foam with independent control of
image size and number of iterations
Parameters
----------
shape : array_like
The shape of the final image to create. To create a 'centered' image,
the shape should be ``3**n``.
n : int
The number of times to iteratively divide the image. This functions starts
by inserting single voxels, then inserts increasingly large squares/cubes.
Returns
-------
im : ndarray
A boolean image with ``False`` values inserted at at the center of each
square (or cubic) sub-section.
Notes
-----
This function may generate a larger image than need then return the center
portion of the requested ``shape``, so the edges may be clipped from the
true Sierpinski foam. This can be avoided by setting shape to some multiple
of ``3**n``.
Examples
--------
`Click here
<https://porespy.org/examples/generators/reference/sierpinski_foam2.html>`_
to view online example.
"""
im = np.zeros(shape, dtype=bool)
if im.ndim == 2:
im[1::3, 1::3] = 1
else:
im[1::3, 1::3, 1::3] = 1
i = 1
pbar = tqdm()
while i < n:
if im.ndim == 2:
mask = np.zeros([3**(i+1), 3**(i+1)], dtype=bool)
s = 3**(i+1)//3
mask[s:-s, s:-s] = 1
t = int(np.ceil(im.shape[0]/mask.shape[0]))
im2 = np.tile(mask, [t, t])
im2 = im2[:im.shape[0], :im.shape[1]]
if im.ndim == 3:
mask = np.zeros([3**(i+1), 3**(i+1), 3**(i+1)], dtype=bool)
s = 3**(i+1)//3
mask[s:-s, s:-s, s:-s] = 1
t = int(np.ceil(im.shape[0]/mask.shape[0]))
im2 = np.tile(mask, [t, t, t])
im2 = im2[:im.shape[0], :im.shape[1], :im.shape[2]]
im += im2
i += 1
pbar.update()
pbar.close()
im = im == 0
return im
[docs]
def sierpinski_foam(dmin: int = 1, n: int = 5, ndim: int = 2, max_size: int = 1e9):
r"""
Generates an image of a Sierpinski carpet or foam
Parameters
----------
dmin : int
The size of the smallest square in the final image
n : int
The number of times to iteratively tile the image
ndim : int
The number of dimensions of the desired image, can be 2 or 3. The
default value is 2.
Returns
-------
foam : ndarray
A boolean image of a Sierpinski gasket or foam
Examples
--------
`Click here
<https://porespy.org/examples/generators/reference/sierpinski_foam.html>`_
to view online example.
"""
def _insert_cubes(im, n):
if n > 0:
n -= 1
shape = np.asarray(np.shape(im))
im = np.tile(im, (3, 3, 3))
im[shape[0]:2*shape[0], shape[1]:2*shape[1], shape[2]:2*shape[2]] = 0
if im.size < max_size:
im = _insert_cubes(im, n)
return im
def _insert_squares(im, n):
if n > 0:
n -= 1
shape = np.asarray(np.shape(im))
im = np.tile(im, (3, 3))
im[shape[0]:2*shape[0], shape[1]:2*shape[1]] = 0
if im.size < max_size:
im = _insert_squares(im, n)
return im
im = np.ones([dmin]*ndim, dtype=int)
if ndim == 2:
im = _insert_squares(im, n)
elif ndim == 3:
im = _insert_cubes(im, n)
return im