s = 0.500 + 10058.000i
Re(s): 0.500
Coarse: 0
Fine: 10058

Help

A visualization of the Riemann zeta function partial sums, highlighting the symmetry between the first several "random walk" partial sums and the congruent clusters at the end.

Press a to see the partial sums across multiple Re(s) values simultaneously, showing how line segments parallel to the real axis (with constant imaginary part) map through the zeta function.

Touch Gestures

👆 Drag with one finger to pan the view
🤏 Pinch with two fingers to zoom in/out
👆👆 Double-tap to reset zoom

Mouse Controls

Drag Pan the view Scroll Zoom in/out Shift+Drag Draw zoom box

Keyboard Shortcuts

r Toggle animation running a Toggle multi-a mode f Toggle full screen d Toggle dark mode e Open/close menu z Reset zoom c Clear history trail h / ? Toggle this help ↑/↓ Adjust a (Re s) ±0.01 Shift+↑/↓ Adjust a (Re s) ±0.1 ←/→ Adjust b (Im s) ±0.01 Shift+←/→ Adjust b (Im s) ±0.1

Controls

a (Real part): Controls the real component of s. The critical line is at a=0.5.

b (Imaginary part): Controls the imaginary component of s. This is animated by default.

Multi-a mode: Shows partial sums across multiple real values simultaneously.

About

This visualization shows partial sums of the Riemann zeta function. The spiral patterns emerge from the complex exponential terms in the sum.