By Tim King · Updated
Random Walk Art Generator
Seeded Brownian Path Drawings, Free PNG
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How the Random Walk Art works
This random walk art generator draws from a wandering point. A random walk is the simplest generative drawing there is: start in the middle, take a step in a random direction, repeat ten thousand times. This page draws the path, shifts the colour as it goes, and lets you save the result as a PNG. It is the picture a physicist means by Brownian motion and the one most people mean by "random walk art".
Random walk art generator: what to know first
Each walker begins at a point and takes a fixed number of steps. Where it can step depends on the walk type. Grid allows only up, down, left or right, which gives the blocky Manhattan look and makes the walker retrace its own path often, so the middle builds up into a dense knot. Free picks any angle for each step, a true two-dimensional Brownian path, wispier and rounder. Smooth keeps a heading and nudges it a little each step, so the path curls in loops rather than jittering; it looks like a doodle rather than static. Walkers that hit the edge of the canvas bounce back in.
Colour shifts along the path so you can read the order the steps happened. Rainbow cycles the hue through most of the wheel from start to finish; the other palettes run through four colours in order. Because strokes are semi-transparent, the places a walker visits repeatedly glow brighter, which is what gives a long grid walk its bright core.
Walkers adds more paths, each starting at a random position and, in Rainbow, its own starting hue. Length is steps per walker, from 2,000 to 20,000. Step size is how far each step goes relative to the canvas; small steps stay compact, large ones range across the whole picture. Line weight thickens the strokes, useful on white backgrounds and at 4K.
Export. Save PNG re-runs the walk at the chosen size with the same seed. Step size is relative to the canvas, so the path is the same shape, just drawn with more pixels. A phone export at 1290 × 2796 is taller than it is wide, and because step size follows the shorter side the walkers cover proportionally more of the height, which suits a lock screen where the clock sits at the top and the icons at the bottom. Nothing is upscaled: every line is re-plotted from the seed at the new size.
FAQ
Why does the walk cluster in the middle?
Because each step is equally likely to go either way, the walker's expected position is where it started, and after n steps it has typically only moved about the square root of n step-lengths away. Long walks therefore wander around the start far more than they travel. That is the actual mathematics of a random walk, not a bug.
Is this the same as Brownian motion?
Brownian motion is the continuous limit of a random walk with tiny steps. Free mode with step size 1 and length 10 is a decent picture of it.
How does this differ from the flow field generator?
A flow field reads its direction from a smooth function of position, so nearby paths move together and look combed. A random walk chooses independently at every step, so its paths are jagged and self-crossing. Smooth mode sits between the two.
Can I get a symmetric picture?
Not directly, but Grid mode with many walkers and a small step size gives an even distribution that reads as balanced. For real symmetry, look at the spirograph and rose curve generators.
See also: all Generative Art tools, Images, Audio, Video & Screen, PDF, SVG, Simulations & Screensavers, Chart Makers, 3D Model Viewers, Drawing Pads, Mockups & 3D Making, Diagram Makers, 3D Science, Tracker Music.
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