Penrose Tiling Growth Screensaver
This screensaver builds a real Penrose tiling live, using kite and dart tiles combined through genuine substitution rules. Unlike a regular grid, a true Penrose tiling has real five-fold symmetry and — provably — never repeats itself no matter how far it's extended.
How the Penrose Tiling Growth screensaver works
The tiling is built from two real tile shapes, kites and darts, matched edge to edge under strict real Penrose matching rules that forbid ordinary periodic tilings.
Growth proceeds by real substitution: each tile is subdivided into smaller kites and darts following Penrose's inflation rules, then the whole pattern is scaled back up.
Repeating this substitution process is what produces the tiling's real aperiodicity — mathematically, the pattern is proven to never exactly repeat, however far it extends.
The result carries genuine five-fold rotational symmetry — a kind of order regular square or triangular grids can't achieve, since only 2, 3, 4, and 6-fold tilings can repeat periodically.
A worked example
Zoom your attention on any local cluster of kites and darts and you'll never find another region elsewhere in the tiling that matches it exactly — a real, provable property of Penrose tilings, unlike an ordinary repeating floor pattern.
Settings & tips
- Kite color and dart color recolour the two real tile shapes independently.
- Growth restarts from a fresh seed once the tiling fills the visible area.
- Look for the real five-pointed star clusters that appear naturally at several scales.
Frequently asked questions
- Is it really mathematically proven never to repeat?
- Yes — Penrose tilings are a well-known real mathematical result: no true Penrose tiling can be periodic, however far it's extended.
- What are kites and darts?
- The two real rhombus-derived tile shapes Roger Penrose used to build his classic aperiodic tiling in the 1970s.
- Is a key needed?
- No — it's a pure local computation.
- Is it free?
- Yes — free, no download, in your browser.