This visualization plots prime numbers on a spiral in 3D space. It demonstrates a property of Gaussian Integers, which are complex numbers `a + bi` where `a` and `b` are integers.
Cyan Primes (p ≡ 1 mod 4):
These are primes that can be factored into Gaussian integers (e.g., `5 = (1 + 2i)(1 - 2i)`). They are plotted as a 3D spiral. Their height on the 'Imaginary' (Y) axis is based on their factorization `p = a² + b²`. You can toggle this displacement using the button in the bottom panel between:
- MAX (a,b): The larger of the two factors.
- MIN (a,b): The smaller of the two factors.
- NORM (√p): The square root of the prime itself.
Yellow Primes (p ≡ 3 mod 4):
These are "standard" primes that
cannot be factored in the complex plane (e.g., 3, 7, 11). They are plotted on the same spiral, but remain flat on the 'Real' (XZ) plane with a height of 0.