Modular times circle i → round(i·k) mod N
Put N dots on a circle and join dot i to dot round(i·k) mod N. At k = 2 the chord envelope is a cardioid, k = 3 gives a nephroid, and every integer k traces a crisp star polygon. Let k drift to watch the machine breathe.
Ulam spiral primes ≤ n²
Walk the integers 1, 2, 3… outward around a square spiral and mark the primes. The faint diagonal streaks are prime-rich quadratic families — most famously Euler's n² + n + 41, prime for every n from 0 to 39.
gap 240+
Hex walk digits → bearings
π's dozenal digits, read as compass bearings — no structure, all texture. Each digit picks one of six hex-lattice directions; each layer re-walks the same stream from an offset start, and the trails blend additively.