The terrain is a synthetic validation-score surface over two hyperparameters: learning rate (log-scaled, front-back axis) and dropout rate (left-right axis). Height and colour (a viridis-style scale — dark purple is worst, bright yellow is best) both encode score. A single narrow ridge holds the true optimum; learning rates that are too small underfit slowly, and rates that are too large destabilise training, so score collapses on both sides.
Bergstra & Bengio's classic 2012 result showed random search finds good hyperparameters faster than grid search in high dimensions — but only if the search space itself is scaled and bounded sensibly, exactly what this simulation lets you test.
A 3D validation-score landscape over learning rate and dropout that you search with grid, log-uniform or naive linear sampling — watch how search-space width, centring and scale choices change how much of the optimum your budget actually reaches.
The landscape has one narrow high-score ridge flanked by underfitting (learning rate too low) and instability (learning rate too high). Log-uniform sampling covers this ridge efficiently; linear-uniform sampling wastes most of its budget near the high end of the range.
Pick a sampling strategy, set your sample budget and search width, then try biasing the box toward high learning rates to see a mis-scoped search space clip the optimum out entirely. The indigo box always marks your defined bounds.
Bergstra & Bengio (2012) showed random search often beats grid search in high dimensions — but that advantage only holds if the search space's ranges and scaling are chosen sensibly in the first place.