The illustrated mathematics guide →
From local rules to a hierarchy at every scale, with ten figures and nineteen worked exercises.
Download for offline readingA hands-on exploration of patterns
Start with a blockDiscover a bigger pattern
Choose a face. Match its arrows. Join the pieces and discover how eight small chairs can become one larger chair.
No installation. No prior knowledge. Undo whenever you like.
One shape. Rules on every face
Your first attachment, one step at a time
- 01
Choose a face
Click the assembly, then choose a face on the moving piece.
- 02
Match the arrows
Compare both faces side by side and turn the piece until they match.
- 03
Attach and explore
Confirm the attachment. Follow hints toward a parent, or build freely.
When you want to go further
Explore the ideas behind the blocks
Look closely at the curved shape →
Rotate the geometric model and inspect the surface features behind the matching rules.
Research notes and evidence →
Browse the arguments, reproducible checks, source code, and open questions.
An activity, and an ongoing research project
The activity models patterns and arrows on a grid. A successful local attachment does not prove an infinite tiling, and the activity does not simulate physical insertion or the detailed curved surfaces.
What has been checked, and whose work is this based on?
The integer-grid model has Lean proofs of unique grouping, legal deflation, translation exclusion, and a bound of 24 proper grid symmetries. The arbitrary-placement and existence arguments for the curved solid remain written mathematics outside that completed formal development. Meshes and printed approximations do not inherit the exact-solid claims.
The discrete matching system agrees with Ioannis Tsiokos’s Chair44 construction under the recorded coordinate correspondence; the physical surfaces differ. This project was developed with substantial AI assistance. AI reviews are not independent human review.
Evidence and attribution