* 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]].