A ratio with the right weight

From a power cost to its perspective

f_p(u) = |u|^p/p becomes P_p(z,r) = |z|^p/(p r^p−1). Change the power; the sublevel sets remain convex.

White contours: 0.1, 0.25, 0.5, 1, 2, 4. A fixed log(1 + cost) color scale is used at every power. The dashed orange slice r = 1 recovers the original function f_p.

Move the pointer over the plot, or focus it and use the arrow keys, to inspect an exact value. Contours are parametrized analytically, not extracted from the heatmap grid.