0af3386Reaction-diffusion on spherical-harmonic surfacesJeremy Magland 1% A dumbbell: a radial profile that pinches at the equator, stretched along z.
2%
3% The radius is 1 - waist*sin(theta)^2, so the poles keep radius 1 and the
4% equator narrows to 1 - waist. Multiplying it into the unit-sphere coordinates
5% raises the degree to 3, which is still far below any lmax the app offers, so
6% the band-limited surface is again the one written here.
7%
8% Two regions of positive curvature joined by a saddle — the first geometry in
9% this list where the Laplace-Beltrami operator differs from the round one in a
10% way that should visibly change where a pattern wants to put its spots.
12function [gx, gy, gz] = shape(theta, phi, waist, stretch)
13 st = sin(theta);
14 r = 1 - waist * (st .^ 2);
15 gx = r .* (st .* cos(phi));
16 gy = r .* (st .* sin(phi));
17 gz = (1 + stretch) * (r .* cos(theta));
18end