Gray-Scott reaction-diffusion, simulated and shown live in the terminal, in C, without any library. Click to drop some chemical, and corals, dividing cells or mazes grow under the cursor.

🇫🇷 Version française

The "mitose" (mitosis) pattern: each spot grows, then splits in two.

Run

make
./rd               # "corail" (coral) pattern
./rd mitose
./rd carte         # the parameter map
./tests.sh         # simulates without a terminal and checks the images

Key	Effect
1 to 9	coral, mitosis, maze, solitons, worms, holes, pulsating, chaos, u-skate
left click (and drag)	drop some V
right click	erase
space	pause
r	restart
c	change palette (violet, magma, ice, moss)
+ -	more or fewer computation steps per frame
m	parameter map
q	quit

You need a terminal with 24-bit colour and mouse support (Konsole, GNOME Terminal, kitty, Alacritty, WezTerm, Windows Terminal...).

Without a terminal, it can also compute a picture (--etapes = steps, --taille = size, palette names are French):

./rd vers --export vers.png --etapes 12000 --taille 300x200 --palette glace

With a .ppm name, the picture comes out as PPM (easier to read back from a script).

What happens

Two chemicals, U and V, are spread over a grid. At each point:

dU/dt = Du·ΔU − U·V² + F·(1 − U)
dV/dt = Dv·ΔV + U·V² − (F + k)·V

• diffusion (Du·ΔU, Dv·ΔV): each chemical spreads to the neighbouring cells, U twice as fast as V;
• reaction (U·V²): where there is some V, it turns U into V (U + 2V → 3V), it feeds itself;
• feed (F·(1 − U)): U is added back everywhere, at rate F;
• kill ((F + k)·V): V is removed at rate F + k.

Just two numbers, F and k, decide the whole landscape. It's the mechanism Alan Turing proposed in 1952 to explain animal spots and stripes.

Map mode (m key): k goes from 0.03 to 0.07 from left to right, F from 0 to 0.08 from bottom to top. Each region of the picture has its own parameters, which shows every regime at once (like John Pearson's map, 1993).

Implementation details

The Laplacian ΔU is approximated by a 3×3 kernel: 0.2 for the 4 direct neighbours, 0.05 for the 4 diagonals, −1 in the middle. The grid is a torus: what leaves on the right comes back on the left. One explicit Euler step, a buffer for the next state, and the pointers are swapped.

Two pixels per character. The ▀ character (upper half block) is drawn with a text colour (the top half) and a background colour (the bottom half), using ESC[38;2;r;g;bm / ESC[48;2;r;g;bm. So one terminal line shows two rows of the grid. Colour codes are only sent again when they change, and the whole frame goes out in a single fwrite.

The mouse. ESC[?1002h asks the terminal to report clicks and drags, ESC[?1006h in SGR format: ESC[<button;x;yM. The terminal is put in raw mode (termios, no echo, no waiting for Enter), on the alternate screen, and everything is restored on exit, even after Ctrl-C. SIGWINCH reports a window resize.

Subnormal numbers. Far from the patterns, V tends to 0 without ever reaching it, and ends up in "subnormal" floats (smaller than 10⁻³⁸), which the CPU handles more than 20 times slower. With parameters where the pattern dies out, a run went from 1.6 s to 40 s. Setting everything below 10⁻²⁰ to 0 fixes it.