Instruments
Interactive tools to hear, see, and feel prime structure. No login required.
Mandelbrot Orchestra
Prime Octave grid · Cosmic Rhythms with 10 toggleable layers · Dual Sequence Voices with oscilloscope · Feed-forward visualisation · 432 Hz
Audio · InteractiveMod-24 Prime Wheel
The fundamental period. 24 spheres, 8 φ(24) spokes where all primes >3 must land. Toggle overlays: 6k±1 pairs, Tusk set, Fibonacci mod 24, factor webs.
Interactive · Core TheoryDynamic Grid Explorer
Drag to reshape the grid width and watch prime columns emerge at mod 6. The "aha moment" tool — see why 6 matters.
SVG · DraggableCircle Ring Explorer
Concentric ring stacking — each ring holds exactly 6n spheres. The hexagonal packing that underpins the prime wheel.
SVG · Geometric3D Sphere & Solids Explorer
Concentric 3D shell packing with prime colouring, plus step-through Platonic Solids builder. Rotatable WebGL.
3D · WebGL · Three.jsTusk Series Explorer
Δ(Σ Pf) — the rhythm of primes and composites. Bar chart spikes for primes, dips for composites. FFT overlay shows peaks at 1/2, 1/3, 1/5. Cumulative walk staircase. Click to connect factors.
Interactive · Core TheoryPrime Horizon
Factor field with numbers along base, potential factors rising. The Prime Horizon (n/2) and Composite Horizon (√n) reveal the sieve structure.
Grid · PatternsAdders & Ladders
The classic board game reimagined — primes are ladders, composites are snakes. Learn which numbers lift you up and which pull you down.
Game · Educational