A collection of visualizations exploring prime number spiral patterns.
Ulam Spiral Möbius Function Prime Gap Riemann zeta function Github
The classic Ulam spiral, discovered by mathematician Stanisław Ulam, revealing diagonal patterns in prime numbers on a square grid.
A variation combining the Archimedean spiral with Ulam's prime visualization, creating a continuous circular pattern.
Prime numbers visualized along polygonal spirals, demonstrating prime gaps and how shape geometry affects pattern emergence.
The path of the Riemann zeta function along the critical line, visualized in the complex plane. Cardioid and spiral visual patterns emerge.
A recursive visualization of "Pioneer" prime symmetries. Drill down into Twin, Cousin, and Sexy prime patterns to see how they evolve.
Numbers laid around a ring where multiplication mod a prime becomes a single rotation. Multiplying repeatedly draws a star polygon.
The Möbius spiral as base (what each number is built from), with sparse markers for significant landings on the multiplication clock mod p. Laps, square residues, primitive roots. Do they align?
Stack many primes instead of one. Pick a number, keep multiplying around each prime's clock: across thousands of primes it takes the "full tour" about 37% of the time, and almost any number does. A steady pattern no single clock shows; g = 5 is the odd one out.