Ulam Spirals
Explore the beautiful patterns hidden in prime numbers through Stanislaw Ulam's famous spiral visualization, discovered during a boring meeting in 1963.
Classic Ulam Spiral
The original visualization with primes highlighted on a square spiral grid
02Animated Growth
Watch the spiral grow number by number, revealing prime patterns
03Interactive Zoom
Pan and zoom to explore millions of primes in the spiral
04Twin Primes
Highlight twin primes (p and p+2) with special colors
05Prime Gaps
Visualize the distances between consecutive primes
06Diagonal Patterns
Highlight the mysterious diagonal lines where primes cluster
07Modular Colors
Color primes by their remainder when divided by various numbers
08Particle Spiral
Primes as glowing particles orbiting in the spiral
09Sieve Animation
Watch the Sieve of Eratosthenes reveal primes on the spiral
10Prime Density
Heatmap showing prime density in different regions
11Hexagonal Ulam
The spiral on a hexagonal grid instead of square
12Sophie Germain Primes
Highlight primes p where 2p+1 is also prime
133D Helix Spiral
The Ulam spiral extended into three dimensions
14Prime Constellations
Connect nearby primes to form beautiful constellation patterns
15Goldbach Spiral
Visualize Goldbach partitions on the spiral
16Palindromic Primes
Highlight primes that read the same forwards and backwards
17Morphing Spiral
Watch the spiral transform between different mathematical bases
18Prime Factorization
Color composite numbers by their largest prime factor
19Lucky Numbers
Compare primes with lucky numbers on the same spiral
20Prime Races
Visualize the race between primes of form 4k+1 vs 4k+3