Planarian Regeneration: Wnt/β-catenin Field Map (2D)

The same neoblast/blastema biology as the 3D worm, viewed as a 2D reaction-diffusion field. A morphogen concentration c(x,t) is integrated on a grid running along the amputated body's anterior–posterior axis with an explicit finite-difference solver — diffusion smooths it, decay clears it, a positional production term P(x) sets the baseline gradient, and a wound source switches on at the cut face as the blastema grows. The live field graph and colored tissue strip show that computation happening, rather than a static formula: suppressing signaling collapses both wounds toward head identity (double-headed), boosting it collapses both toward tail identity (double-tailed), exactly reproducing the textbook RNAi phenotypes from the field's own dynamics.