49 lines
2 KiB
Org Mode
49 lines
2 KiB
Org Mode
* Reaction-Diffusion Model
|
|
|
|
[[https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_system][Reaction-Diffusion system]] simulation using the Gray-Scott model, in [[https://www.dyalog.com/][Dyalog APL]] and [[https://mlochbaum.github.io/BQN/index.html][BQN]].
|
|
|
|
[[img.png]]
|
|
|
|
** Running the Dyalog version
|
|
|
|
[[https://www.dyalog.com/download-zone.htm][Install Dyalog APL]] and [[https://en.wikipedia.org/wiki/Netpbm][Netpbm]] (~apt-get install netpbm~). Then run
|
|
~make~. This will create the =img.pnm= and =img.png= files in the
|
|
current directory.
|
|
|
|
The images are generated from APL by creating a [[https://en.wikipedia.org/wiki/Netpbm][Netpbm]] file, which are
|
|
nice because they are just plain-text. It is then converted to PNG
|
|
using ~pnmtopng~.
|
|
|
|
** Running the BQN version
|
|
|
|
Clone [[https://github.com/dlozeve/bqn-graphics][bqn-graphics]] at the same level than this repository. Run the
|
|
=./generate_animation.sh= script. It requires [[https://www.gnu.org/software/parallel/][GNU Parallel]], [[https://en.wikipedia.org/wiki/Netpbm][Netpbm]],
|
|
and ffmpeg.
|
|
|
|
PNM and PNG images are in the =out= directory, and the animation is in
|
|
=out.mp4=.
|
|
|
|
** Parameters
|
|
|
|
All the parameters are defined directly in [[grayscott.dyalog]].
|
|
|
|
The parameters of the model are:
|
|
- ~dt~: the time step,
|
|
- ~da~: the diffusion rate for A,
|
|
- ~db~: the diffusion rate for B,
|
|
- ~f~: the feed rate for A,
|
|
- ~k~: the kill rate for B.
|
|
|
|
Additionally, you can change ~N~, the size of the grid, and ~steps~,
|
|
the number of time steps to simulate.
|
|
|
|
Finally, the function ~mat2pbm~ exports to a bitmap (black and white)
|
|
format, while ~mat2pgm~ exports a grayscale image.
|
|
|
|
** References
|
|
|
|
[[http://www.karlsims.com/rd.html][This page]] gives a good explanation of the Gray-Scott model. [[https://github.com/EnvModelling/Env_modelling/blob/master/Spatio-temporal-modelling/Reaction_diffusion_2D.ipynb][This
|
|
notebook]] gives a nice example of implementation in Python with
|
|
Numpy. For even more details on the model and a classification of
|
|
pattern, see [[http://mrob.com/pub/comp/xmorphia/][this page]].
|
|
|