Generative Art and Mathematical Curves

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Seeds

Random art is only useful if you can get the same result twice. Each generator starts its random number generator from the seed in the rail, so the picture depends only on the seed and the sliders. Regenerate picks a new seed; typing a seed you saved earlier brings its picture back. Because the drawing is done in relative coordinates, the export at 4K is the same composition as the preview, not a crop of it.

Noise-based art

The wallpaper, abstract, flow field, texture and random walk generators all lean on Perlin noise, a smooth random function that changes gradually across space. Sample it slowly and you get clouds; take its gradient and follow it and you get the flowing lines of a flow field; stack several octaves and you get marble and wood grain. These pages are the ones to try when you want a background rather than a diagram.

Mathematical curves

Spirograph, Lissajous, harmonograph and rose curves are parametric equations plotted with a pen. They need no randomness at all; the seed only picks starting parameters, and the sliders are the actual maths — gear ratios, frequencies, damping, petal counts. Small integer changes make very different shapes, which is what makes them fun to poke at.

Fractals

The L-system tree, Sierpinski triangle and Koch snowflake are built by applying a rule repeatedly; the depth slider is the number of times. The Mandelbrot and Julia explorers are computed pixel by pixel from a complex-number iteration; click to zoom in and the detail keeps coming. Deep zooms take a moment at 4K because every pixel is a loop.

Export

Save PNG re-renders the picture at the size chosen in the rail — common desktop and phone resolutions, or the preview size — and downloads it. Nothing leaves the browser; there is no upload and no account.

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