A heatmap of |ζ(σ + it)| across the critical strip 0 ≤ σ ≤ 1. Bright bands of magnitude wrap the strip; the dark notches on the critical line σ = ½ are non-trivial zeros — places the universe says "primes go here, not there."
ζ(s) = η(s) / (1 − 2^(1−s)), where η(s) = Σ (−1)ⁿ⁻¹/nˢ converges everywhere in the critical strip. Each pixel is one evaluation. The bright vertical band at σ = 1 is the pole — ζ blows up there. The dark spots on the critical line σ = ½ are non-trivial zeros: 14.13, 21.02, 25.01, 30.42, 32.94, 37.59, …
σ = ½. We've verified this computationally for the first ~10¹³ zeros, but a proof has resisted 165 years of attack. If you switch to phase mode, you can see ζ wind around 0 — and each zero is a singular point where every color of the rainbow meets in a Riemann-sphere-like pinch.