Local optimaâ
Global peak fitnessâ
Hill-climb finds bestâ
fitness low high
global optimum
other local optima
Stuart Kauffman's NK model is a dial for ruggedness. Each of N genes contributes to fitness depending on its own state and K others, so K is how much each gene's effect depends on the rest (its epistasis). At K = 0 the landscape is smooth: nearby genotypes have similar fitness, so hill-climbing always finds the top, like the weasel. Crank K up and it dissolves into noise, a mass of local optima: deceptive traps like HIFF. Drag the slider and watch it happen.
Sweeping K from 0 to Nâ1: local optima multiply (roughly 2N/(N+1) at maximum epistasis), while the odds of a hill-climber reaching the global optimum collapse toward zero. This is Kauffman's complexity catastrophe: beyond a point, more interdependence between genes makes good solutions undiscoverable by local search. It's the quantitative reason recombination and other global operators matter, and the bridge from the weasel to HIFF.
At zero epistasis the heatmap shows clean stripes, not a blob. Fitness is a plain sum of independent genes, so each axis just adds its own bands: one smooth peak, a 100% basin, hill-climbing never fails.
The "hill-climb finds best" stat falls off a cliff as K rises. More peaks means each basin of attraction is smaller, so a random start almost never drains to the global one. The landscape is searchable but the answer is unfindable.
Global-peak fitness actually rises with K before levelling off: a little epistasis creates taller peaks, but too much shatters the basins so you can't climb them. Complexity has a sweet spot.