Random Point Generator
Scatter a set of random points inside a rectangle or circle and see them plotted live — useful for generative art, sampling, and simulations.
Generate
How the Random Point Generator works
Generating uniformly random points inside a circle is trickier than it looks: naively picking a random angle and random radius clusters points near the centre, because area grows with the square of the radius. This tool instead uses rejection sampling — drawing random (x, y) pairs inside the bounding square and discarding any that fall outside the circle — which correctly produces uniform density across the entire circular area.
This technique has real uses beyond visual generative art: uniform point sampling within a region underlies spatial simulations, procedural generation in games, and Monte Carlo integration methods like the Pi estimator elsewhere in Xrandom's Statistics section.
How to use it
Frequently asked questions
Why use rejection sampling for the circle?
It's the simplest method that guarantees a truly uniform distribution across the circle's area; simpler angle-and-radius approaches introduce a bias toward the centre unless carefully corrected.
Can I export the coordinates as numbers?
The current view is visual; for raw coordinate values, the Random Decimal Generator can produce independent x and y values in a 0–1 or custom range.
What's a practical use for this?
Procedural art, seating or layout randomization, spatial sampling for simulations, and visual demonstrations of uniform distribution.