Python implementation of the Color Stealing algorithm. In short, this technique constructs aesthetically pleasing fractals by copying color patterns from a given auxiliary image to a binary fractal.
Definitely not a cherry-picked sample.
Perhaps the most simple method to construct a fractal image is the Chaos Game. A fractal can be defined by its iterated function system (IFS), which is a set of n functions. For images, each function is with a corresponding probability
. The Chaos Game begins by sampling a random 2d coordinate
. At the j-th iteration, an integer
is sampled based on the distribution p. The next coordinate is computed as
. This coordinate is then plotted on a 2d grid, which was initially empty. After a number of iterations, the result is a binary image. Examples of such images can be found in the second column of the generated samples as well as at
templates/images.
The Color Stealing algorithm extends the Chaos Game by adding color to the constructed fractal. This requires an auxiliary image as input. Specifically, two IFSs are kept: one with functions and probabilities
for the fractal image and one with functions
and no probabilities for the auxiliary image. Similarly, two coordinates are initially sampled:
. At the j-th iteration, an integer
is likewise sampled from the distribution p, which is followed by calculations
and
. Then the fractal is extended:
. This process eventually results in images such as the third column of generated samples.
Below is a list of examples constructed by the provided scripts. Each sample was generated using the command python run.py -s -i 100000 -nt -l <ifs_path> -c <img_path>, where <ifs_path> was chosen from templates/ifs and <img_path> from assets/auxiliary. Running this commands produces a different result each time, due to rng. Obviously, all the examples are cherry-picked.
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git clone https://github.com/davidsvy/color-stealing
cd color-stealing
pip install -r requirements.txt
python run.py OPTIONS
-s, --save [FILE_NAME] If provided, saves the image and the IFS.
If FILE_NAME is not given, the image will
be saved at DIR/images/TIMESTEP.png and
the IFS at DIR/ifs/TIMESTEP.csv. DIR is
the next argument and TIMESTEP is the
timestep at the time of saving the files. If
FILE_NAME is given, the image will be saved at
DIR/images/FILE_NAME.png an the IFS at
DIR/ifs/FILE_NAME.csv. For the script to run,
either -p or -s must be provided.
-d, --dir DIR Directory where the image & the IFS file will
be saved.
-p, --plot If given, the constructed fractal will be
rendered using plt.imshow(). For the script
to run, either -p or -s must be provided.
-cm, --cmap CMAP cmap for for plt.imshow(). Accepted values are
'i', 'p', 'm', 'c', 'v'. Default value is 'i'.
CMAP is ignored if either -f or -c is provided.
-r, --resolution RES Resolution of the square fractal image. Default
value is 1024.
-b, --batch_size BS Number of points calculated at each iteration.
If -f is given, setting BS <= 4 might result in
better visuals. Default value is 128.
-i, --n_iter N_ITER Number of iterations for the chaos game algorithm.
Default value is 50000.
-ni, --n_ignore N_IGNORE Number of initial iterations that will not be
rendered. Default value is 200.
-nt, --no_tqdm If given, the tqdm progress bar will not be used.
-l, --load PATH If not provided, the scripts will sample a random IFS.
If provided, the fractal stored inside PATH will be
generated. PATH must be a path to a valid IFS csv
file.
-m, --mutate PATH Same as the previous argument, with the difference
that the loaded IFS will be slightly mutated in a
random fashion.
-c, --color_steal PATH If not provided (and -f not provided), a binary
fractal will be generated. If provided, the fractal
will be constructed by copying color patterns from
the image stored at PATH using the Color Stealing
algorithm.
-f, --flame If not provided (and -c not provided), a binary
fractal will be generated. If provided, the image
will be generated using the Fractal Flame
algorithm. Unfortunately, this mechanic is not
working well yet. Setting BS <= 4 might result in
better results.
-g, --gamma GAMMA Gamma parameter for the fractal frame algorithm.
Default value is 20.
-su, --sup SUP Supersampling ratio for the fractal flame algorithm.
Default value is 3.
The author of this repo can be mailed at dsvyezhentsev@gmail.com.
@inproceedings{Barnsley2003ERGODICT,
title={ERGODIC THEORY , FRACTAL TOPS AND COLOUR},
author={Michael F. Barnsley},
year={2003}
}