Sierpinski Triangle Generator — SVG Fractal, Free
Generate the Sierpinski Triangle to any depth. Famous self-similar fractal, exported as SVG. Browser-only.
About Sierpinski Triangle Generator
The Sierpinski Triangle is a classic fractal: take an equilateral triangle, remove the central upside-down triangle, repeat on each remaining sub-triangle, repeat again. After infinite iterations, the result has zero area but infinite perimeter — a fractal of dimension log(3)/log(2) ≈ 1.585. The ZTools Sierpinski Triangle Generator draws the construction live in SVG up to depth 9 (19,683 triangles), with custom colours, sizes, and optional chaos-game generation as an alternative to recursion.
Use cases
- Math classroom — illustrate fractals. Increment depth from 0 to 7 to show how iteration produces the fractal. Visually unforgettable.
- Generative wall art. High-depth Sierpinski with custom colours produces striking minimalist art.
- Algorithm viz. Demonstrate divide-and-conquer / recursion visually. Each call splits the problem into 3 sub-problems.
- Teach Pascal's Triangle connection. Color Pascal's Triangle entries by parity (odd/even) — the pattern that emerges IS the Sierpinski Triangle.
How it works
- Pick depth. 0 = single triangle. 1 = 3 sub-triangles. N = 3^N triangles.
- Choose colours. Single fill or gradient by depth (top triangle one colour, deeper sub-triangles another).
- Pick generation method. Recursive (exact, deterministic) or chaos game (random — converges to the same shape after ~10,000 points).
- Export. SVG (clean vector), PNG (rasterised at chosen size).
Examples
Input: depth 5, recursive
Output: 243 small triangles arranged in the famous self-similar pattern.
Input: depth 7, recursive
Output: 2,187 triangles — fine detail visible at high res.
Input: chaos game, 10,000 points
Output: Each point random + halfway-to-vertex; result converges to the Sierpinski shape after ~5,000 iterations.
Frequently asked questions
What's the chaos game?
Pick 3 vertices (corners of an equilateral triangle). Start at any point. Repeatedly: pick a random vertex, move halfway towards it, plot. After thousands of iterations, the plotted points form the Sierpinski Triangle. Counter-intuitive but provably correct.
Pascal's Triangle connection?
Color row n column k of Pascal's Triangle black if C(n, k) is odd, white if even. The resulting pattern is a Sierpinski Triangle (visible from row 16 or so).
How big can depth be?
9 in this tool (19,683 triangles). Beyond, SVG path count causes lag. For higher depth, use the chaos game with 100,000+ points.
Privacy?
All in browser.
Pro tips
- For teaching, animate from depth 0 to depth 5 — each step is dramatic.
- Chaos game shows that randomness can produce structure — counter-intuitive demo for students.
- Connect to Pascal's Triangle visually — same fractal, two derivations.
- Export SVG for slides; PNG only when a raster system needs it.
Reviewed by Ahsan Mahmood · Last updated 2026-05-06 · Part of ZTools.
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