Fractal Generator
Three classic fractals, built by their real constructions. Pick a curve, step the iterations up, and take the SVG or PNG.
Local onlyEverything on this page — the preview, the randomness, and every file you download — is generated by JavaScript in this tab. Nothing you type, pick, or upload is transmitted, and the page keeps working offline.
These are the fractals from the textbooks, drawn by their actual constructions rather than traced from pictures. The Koch snowflake replaces every edge with four smaller edges, each iteration tripling the shape's detail. The Sierpinski triangle removes the middle of every triangle, forever. The dragon curve is what a strip of paper folded in half n times looks like unfolded — a single line that never crosses itself yet fills space. The iterations slider steps each construction from its first obvious move to the level where the eye gives up counting.
Each curve keeps its own sensible iteration range so the export stays a clean, usable file — the point where more iterations only add kilobytes, not visible detail, is where the slider stops. The snowflake and triangle export as filled shapes with your gradient; the dragon exports as a stroked path. All three are single-path SVGs, which makes them fractal design assets rather than screenshots: they scale from a favicon to a poster without losing a pixel, and there's a 960×960 PNG for raster-only tools.
Questions this tool gets asked
What is a fractal?
A shape whose detail repeats at every scale — zoom into a piece and you find a smaller copy of the whole. The three here are the classic constructed fractals: each is defined by a simple rule applied over and over, and each iteration of the slider is one more application of the rule.
How is the Koch snowflake constructed?
Start with an equilateral triangle. On every edge, replace the middle third with two sides of a smaller equilateral triangle pointing outward. One iteration turns 3 edges into 12; six turns it into a shape with a finite area but a perimeter that grows without bound — the classic coastline paradox in miniature.
What is the Sierpinski triangle?
Take a filled triangle, remove the upside-down triangle formed by the midpoints of its sides, and repeat on the three filled triangles that remain. The result has zero area in the limit but infinite edge — and it shows up unexpectedly in Pascal's triangle, cellular automata, and chaos-game plots.
What is the dragon curve?
Fold a strip of paper in half repeatedly, unfold every crease to a right angle, and look at the edge: that path is the dragon curve. It never crosses itself, and four copies of it tile the plane. It appeared famously on the chapter pages of Jurassic Park. The slider is the number of folds.
Why is the iteration slider capped differently per curve?
Each construction grows at a different rate — the snowflake quadruples its points per step, Sierpinski triples its triangles, the dragon doubles its segments. The caps sit where the SVG is still a clean, reasonably sized file and further steps add no visible detail at screen or print sizes.
Can I use these fractals commercially?
Yes — the mathematics is centuries old and what you generate is yours: posters, textbooks, slides, T-shirts, anywhere. The SVG and PNG are produced entirely in this tab, free, with no watermark or attribution required.