What this is

A 3D lab for fractals made by folding and scaling space. Each shape is a Mandelbox, Amazing Surf, Surf Mod1 or Box Julia fractal, drawn live on the GPU.

Nothing is a recording. Every slider changes the formula, and the Math card shows the formula you are looking at.

The ideas, in plain words

• Box fold: each coordinate is folded back inside a limit, like a mirror.
• Sphere fold: points inside a small sphere are blown up; points outside a big one are left alone.
• Scale and shift: the space is stretched, then moved, and the loop repeats.
• Distance estimate: how far the nearest surface is, found without drawing every point.

How to use it

• Drag the canvas to turn the object, or scroll to zoom. Pinch works on touch.
• Pick a fractal in Style. Each one shows only its own controls on Simple.
• Finish sets the colour from the template palettes. Iridescent colours by depth.
• Motion moves the camera or the shape on its own. Dragging the canvas stops it.

Where these ideas show up

• Computer graphics: ray marching, distance estimates and lighting.
• Mathematics teaching: iteration, self-similarity and how a small rule builds a large shape.

What it is not

A visual and teaching tool. It is not a physics model and not a prediction tool.

© 2026 UUON Foundation Inc. · Phillip Aguilar Ruiz III · USAL-1.0 · Fractal forms credit Tom Lowe (Mandelbox, 2010) and Knighty (Amazing Surf, 2011).