Class Tangle Float

Red and blue dots tangled in 2D — no line can separate them. Plant radial kernels. Red dots rise. Blue dots sink. Find the separator hiding in a third dimension.

Class Tangle Float gives you a scatter of red and blue dots and an impossible problem — separate them without a straight line.

The dots are arranged in patterns no boundary can divide in two dimensions. Blue dots form a ring around a cluster of red ones. Red dots occupy opposite corners of a grid while blue dots occupy the other two. Two crescent shapes interlock, each hugging the other's curve. These are the classic configurations of machine learning — the patterns that break every simple classifier and require something more.

That something more is a kernel.

Tap anywhere on the three-dimensional ground plane and a golden pillar appears. It is a radial basis function — a kernel point — and it immediately affects every dot on the plane. Red dots near the kernel rise upward. Blue dots near the kernel sink downward. The effect fades with distance according to a Gaussian curve, so dots close to the kernel respond strongly and dots far away are barely touched. The differential — that nearby dots of the correct class rise much more than distant dots of the wrong class sink — is what creates the separation.

The ground plane is the separator. When every red dot floats above it and every blue dot hangs below it, the problem is solved. A boundary that looked impossible in two dimensions becomes trivially flat in three. The kernel trick is a mathematical sleight of hand that has powered image recognition, text classification, and bioinformatics for decades. Class Tangle Float makes it physical.

Placing the first kernel near the red cluster at the centre of the ring pattern is immediately satisfying. The red dots lift. The surrounding blue ring drops. The ground plane lights up as dots cross to their correct sides. Understanding why it worked — that proximity to the kernel, not the kernel itself, creates the separation — is the first genuine insight into how support vector machines think.

The gamma slider controls how tightly focused each kernel's influence is. At high gamma, each kernel affects only its immediate neighbourhood — good for complex tangled patterns, requiring precise placement. At low gamma, each kernel spreads broadly across the plane, useful for simpler configurations but prone to pulling distant wrong-class dots in the wrong direction. Finding the right gamma for each puzzle is the second layer of strategy.

Each puzzle allows a limited number of kernel placements. The budget forces deliberate thinking — not placing kernels until you understand which clusters most need lifting, and how the placement of each kernel will affect the global distribution. Running out of budget with some dots still on the wrong side of the plane is a lesson in spatial reasoning that no classroom can replicate.

Three built-in patterns progress from introductory to genuinely difficult. Beyond them, procedurally generated tangles ensure no two sessions are the same.

The mathematics behind this game is used every day to classify cancer cells from healthy ones, spam from email, faces from backgrounds, and fraudulent transactions from legitimate ones. Class Tangle Float gives you the geometric intuition that makes all of it make sense — not through explanation, but through play.

No ads. No equations shown. No machine learning knowledge required to start.

Just the dots, the ground, and the kernel that lifts everything into place.