A sphere with bumps

With “Amount of deformation ε” at 0 the sphere is smooth and K is 1 everywhere. Drag it up and four bumps rise out of the sphere while two dents sink in. The colour follows K: dull gold around K = 1, turning coral as K grows, dark near 0, ice-blue where K < 0. On the tops of the bumps K is always larger than 1. The floor of a dent first flattens, K dropping to about 0; push ε further and the floor curves into a bowl, K turns positive again, and near the top of the slider the largest K of all sits at the bottom of a dent. Once ε passes about 0.34, saddle-shaped patches appear round the bumps and dents, where K < 0 and the surface turns ice-blue; from then on the smallest K in the corner is negative. The corner gives the largest and the smallest K at this moment, and its last row is the total curvature, K added up by area over the whole surface. K and area change everywhere, but the surface stays smooth and closed and gains no holes, so however far you drag ε, the total stays 4π. The sphere turns slowly by itself; drag “Turn the view” to go round it and look at the bumps and dents.