A logo that thinks in four dimensions

Look up. The thing rotating at the top of this page is a tesseract — a cube's older, stranger sibling, the four-dimensional hypercube. You are not seeing it. You cannot see it; your eyes end at three dimensions. What you are seeing is its shadow, cast down one dimension the way a wire cube throws a flat tangle of lines onto a wall.

That shadow has a name mathematicians gave it a century ago: the Petrie projection. Point a hypercube down its longest diagonal, let it fall onto the page, and its sixteen corners arrange themselves into a perfect eight-fold star. Every straight line you can trace in the mark is one of the tesseract's thirty-two edges, caught mid-fall. It is not a decoration of a four-dimensional idea. It is the four-dimensional idea, minus one dimension, told without a single lie.

§ 01Sixteen corners, thirty-two edges, zero pixels

Here is the part that should stop you. This mark is not an image file that someone nudged into shape in a design tool. It is computed — about fifty lines of plain code that place every vertex at a corner of four-dimensional space, join the ones that differ in exactly one coordinate, and flatten the result. Change one number and the whole figure regenerates, razor-sharp, at any size from a favicon to a billboard. The logo is source code. It has no native resolution because it has no pixels to run out of.

The consequence is quiet but total: the mark can never blur, never pixelate, never look "low-res." A four-dimensional object rendered as mathematics is as crisp at ten metres as at ten centimetres, because at every scale it is being solved, not enlarged.

§ 02Why it moves

A still tesseract is a paradox you can frame. A turning one is a paradox you can watch happen. Give the shape a rotation in one of its ordinary planes and it tumbles the way any object would. But a hypercube has planes we don't — planes that turn through the fourth direction — and a rotation there does something no solid object can: the inner cube swells, passes through the outer one, and trades places with it, all without anything tearing.

The colour is the tell. Each line is tinted by how deep it sits along the axis you cannot point to — cold and blue where the shape recedes into the fourth dimension, warm and gold where it leans toward you. So the invisible direction stops being a rumour and becomes something your eye can follow. Watch the figure open into its unfolded net and every colour drains to a single hue: proof, in pigment, that a flattened hypercube truly has surrendered its fourth coordinate.

§ 03The cross that Dalí painted

Unfold a paper cube and it falls flat into six squares — a little crucifix of cardboard. Unfold a tesseract and its eight cubic cells fall into three-dimensional space as an eight-cube cross. Salvador Dalí painted exactly this shape in 1954 and hung a figure upon it, an object from a dimension we can't enter standing in for a mystery we can't hold. The mark above can perform that unfolding on command, hinging its cells apart and closing them again, and the geometry has been checked every way it can bend.

The controls for all of this are one tap away — the button in the corner opens the full instrument: six planes of rotation, the fold, the fractal echoes that repeat the shape through its own turning, and a way to save any moment you like and string those moments into an animation of your own.

Rendered live from the motion lab · built from the logo generator · open source on GitHub
Sixteen vertices. Thirty-two edges. One theorem, any resolution.