Mathematical Morphology is D'Arcy Thompson's gift to the world. The idea that biological shape is just geometry that evolution discovered first. That is why Morphogenesis; the study of how living things get their shapes. How a flat sheet of cells becomes a hand. How a spore decides to branch left or right. The word literally means the origin of form.
We can use math and logic to explain why living systems look and behave the way they do.
Animated biological forms from equations, computer-generated shapes that look so biological your brain cannot separate them from life.
Below is a membrane dynamics and pseudopod formation. showing that biology has equations for that too.
In the video below, the Amoeba pulses with a green bioluminescent glow. The boundary never stops morphing, nucleus drifting inside, vacuoles orbiting slowly. 5 overlapping sine waves, each spinning at a different speed. None of them know about each other. The mess they create together looks alive.