Art of PDEs

Kovalevskaya on Chaos

Playing in time and space

$\pd{\psi}{t}=(D_r+\i D_i)\nabla^2 \psi+(a_r+\i a_i)(1-I_S(x,y))\psi+(b_r+\i b_i)\psi|\psi|^2$

Turing on Turing

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$\pd{u}{t}=\nabla^2 u+(1-T(x,y)) - u + u^2v$, $\pd{v}{t}=D\nabla^2v+ 1 - u^2v$

We ❤️ PDEs

Beating hearts and slime moulds

$\pd{u}{t}=\nabla^2 u+$❤️

Chemical Basis of Morphogenesis

A transformative text

$\pd{u}{t}=\nabla^2 u+a-u+u^2v$, $\pd{v}{t}=D\nabla^2v+ b-u^2v$

Spiral waves

You spin me right ’round, baby

$\pd{u}{t}=D_u\nabla^2 u+au-(u+cv)(u^2+v^2),$ $\pd{v}{t}=D_v\nabla^2v+av+(cu-v)(u^2+v^2)$

A-maze-ing PDEs

Searching for love in all the wrong places

$\pd{🐀}{t}=D_🐀\vnabla\cdot (\vnabla 🐀-g(🐀)\vnabla🧀)+f(🐀,🧀),$ $\pd{🧀}{t}=D_🧀 \nabla^2🧀+g(🐀,🧀)$