# Psychedelic Animations using Trigonometry

We will in this post showcase a method for generating psychedelic animations using the basic trigonometry functions sin(x), cos(x) and tan(x).

By animation, we mean a smoothly blending series of images of a given size. Suppose we just want to create a single image, we could define a function of two dependant variables f(x, y), where x and are the coordinates of a given point on the image. This means that the function depends on the x and coordinates, giving a smooth variation across the image.

Here is the image representing f(x, y) = x + y:

The brightness of a pixel is 256 – f(x) mod 256

This is nice. It’s a smooth image, however, it’s not very “psychedelic”. To accomplish this, we construct not one, but three functions R(x, y), G(x, y) and B(x, y) – one for each color channel. This produces the following image instead:

R(x, y) = sin(x+y)   G(x, y) = cos(x+y)  B(x, y) = sin(x) + cos(y)

This is perfect! This is trippy enough for our purposes, however, it’s not very “animated”. This is a single image, so it doesn’t really count as an animation. To make this an animation, we introduce another independant variable t (for time), so we get three functions R, G, B, dependant on three variables x, y, t. Introducing a time variable, produces animations like the follow:

Fewer colors in this than the actual version, due to .GIF file format

This is perfect! We can now construct animated psychedelic animations using math!