f(z) = z -z 1/z z^2 animated squaring z^3 z+exp(i*seconds()) (z+1)/(z-1) 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

Here you see how the stereographic projection of a sphere onto a plane is obtained. For each point on the surface, a ray from the north-pole through this point is constructed. The intersection of the ray with the plane is the projected point (use R to make this ray visible).

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

Controls:

I:	Invert sphere.
R:	Show Ray.
C/M:	Change the input mode. By pressing C once, you can map a spherical image to the sphere. A further C maps 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 to this applet and use them as texture.
L:	Show (2 pi i)-periodic lines
A/B:	Decrease or increase height of sphere.

You can also view, how the world looks like inside the sphere (spherical view)

Applet made with CindyJS. Author: Aaron Montag.