reaction diffusion equations

Hi!
Lately there was a nice BBC documentary on YT about the math of chaotic
patterns "The Secret Life of Chaos".
https://www.youtube.com/watch?v=VYHSgLpziH0
But it looked like they had some errors in the reaction diffusion equations (like the i,j indices in the second equation without an associated variable):
https://www.youtube.com/watch?v=VYHSgLpziH0
https://i.imgur.com/NByWRl6.png
I've downloaded Turings paper they are referencing,
"THE CHEMICAL BASIS OF MORPHOGENESIS".
But I'm not sure how the equations given there match up
with the equations displayed in the BBC documentary.
https://i.imgur.com/GoACqji.png
Maybe other videos on youtube give a better demonstration of
how equations along these lines can yield interesting visual
patterns.
https://www.youtube.com/watch?v=BV9ny785UNc
https://www.youtube.com/watch?v=COMvgTLTw6g
Is there any math wizard out there who can provide a quick
interactive demo version in desmos or geogebra?
https://www.shadertoy.com/view/WlSGzy