The gyroid is a triply periodic minimal surface defined implicitly by f(x,y,z) = sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = 0. A standard way to understand a 3D implicit surface without rendering it in 3D is to fix one coordinate and look at the resulting 2D level-set curve — exactly what this page does: for a chosen z, it plots the plane curve where f(x,y,z) = 0 as x and y vary, using the marching squares algorithm to trace the contour on a live grid.
As the z-slice sweeps from 0 to 2π, the contour's topology changes continuously — closed loops merge, split, and reconnect — visualising how the gyroid's two interpenetrating labyrinthine channels weave through space. The coloured regions on each side of the contour show the sign of f(x,y,z): one colour marks the "inside" channel, the other the "outside" channel, the same two networks that appear as separate solid volumes in the full 3D marching-cubes rendering.
This is the same field used by the 3D Gyroid & Minimal Surfaces explorer, just sliced rather than volumetrically meshed — a lighter, Canvas2D-only way to explore the same mathematics on any device.