f(z) = z -z conjugate(z) 1/z z^2 animated squaring z^3 z+exp(i*seconds()) (z+1)/(z-1) z^4+1/(z^4) z^5-1 sin(z) exp(z) exp(mod(z,2)) exp(mod(log(z),2)) exp(mod(z*(2+2*pi*i)/(2*pi*i),2)) exp(mod(log(z)*(2+2*pi*i)/(2*pi*i),2)) Droste Droste +zoom twisted Droste twisted Droste +zoom squared Droste twisted squared Droste Mandelbrot set

You are inside a sphere, which you can rotate by dragging the mouse.

If you enter a complex function, it is pulled back through the stereographic projection. Each pixel with complex coordinate z on the sphere gets the color of the pixel with coordinate f(z) on the sphere. You can select some example functions from the dropdown box.

Controls:

C/M:

Change the input mode. By pressing C once, you can map a texture of the earth to the sphere. If you have a spherical camera (such as the Ricoh Theta), then you can use the spherical footage instead with pressing C multiple times. You can also drag and drop your spherical images and use them as texture.

Applet made with CindyJS. Author: Aaron Montag.