ana
four-dimensional widgets
Ana and kata are Hinton's words for the two ways along the fourth direction of space, the way up and down are the two along the third. This is a shelf of small instruments for looking that way: each one a single object or idea in four dimensions that you can turn, slice through and read numbers off, with the 2D and 3D versions beside it to calibrate your eye.
Every widget's mathematics lives in a module with no page attached, and a node selftest holds it to what the page claims.
Widgets
HILBERT4 turn it
One unbroken path through every cell of the unit tesseract, each step to a cell that shares a face. Cut every cell in sixteen and the path becomes sixteen turned copies of itself, joined end to end, down to a million cells. See its shadow, or cut its hypertubes with your 3D slice and watch them appear as blobs, swell and vanish; twist the slice into w with the pad and move it ana and kata with the lever. Thicken the tubes to read it, and scrub along the path to read each cell's place as base-16 digits, one per level of the nesting. The same code draws the square and the cube.
MANDELBRACT four ways
The Mandelbrot set in four dimensions. There is no 4D number system that does what the complex numbers do, so it splits four ways, each giving something up. The honest one is the (c, z₀) space, where the Mandelbrot set and every Julia set are perpendicular planes through one object: twist your slice and one turns into the other. Then the bicomplex set (the Mandelbrot set times itself), the quaternion set (it, spun round), and the hyperbulb (the Mandelbulb's trick, a dimension up). Sphere-traced solids, cut open to show the plane inside.