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Precision limit reached. Past about 1013× the computer's numbers run out of digits, so pixels start to repeat and it goes blocky.
Tap a spot to see its Julia set
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width 3.4
Iterations
drawing…
Famous spots
Your bookmarks
How to play
- Pinch, scroll or double-tap on a glowing edge to dive in.
- Keep going. The detail never runs out.
- Turn on Julia mode and tap a spot to see its Julia set.
| Do this | Phone | Keyboard |
|---|---|---|
| Zoom in | Pinch out, or double-tap | + (or mouse wheel) |
| Zoom out | Pinch in | - |
| Move around | Drag | Arrows (on the stage) |
| Julia set | Julia mode, then tap | J (uses the centre) |
| Bookmark | Bookmark button | B |
| Start again | Reset | 0 |
What's happening?
- Every pixel is a number. The computer takes it, squares it and adds the start number back, again and again.
- If the answer stays small forever, the pixel is in the set: it's painted dark.
- If the answer shoots off to infinity, the colour shows how fast it escaped.
- That one tiny rule makes a shape whose edge has endless detail. Zoom in anywhere on the edge and you'll find new spirals, and even tiny copies of the whole set.
- A Julia set uses the same rule, but keeps one number fixed. Each spot on the Mandelbrot set has its own Julia set. Spots inside give solid shapes; spots outside give dust.
- The computer only keeps about 16 digits. At about 1013× zoom it runs out, and the picture goes blocky.
Try this: find a tiny copy of the whole Mandelbrot set hiding somewhere along the edge. Hint: follow the long spike on the left. Bookmark it when you do!