Approaches

Scanline and direct

When creating an image there are two main methods:

• scanline methods: all pixels in the image will be scanned. For each pixel, the color has to be determined. The coordinates of the pixel are converted into mathematical parameters. Then an algorithm is run on that parameter. For instance we may have a dynamical system, the point may represent a point in phase space, whose orbit we simulate/iterate, and the color of the pixel will be chosen according to the behaviour of the orbit.

• direct drawing: points, lines or areas, are determined by their mathematical coordinates, converted into pixel coordinates, and drawn

A vast majority of my images use scanline algorithms.

Backward and forward iteration

This concerns discrete dynamical systems.

Forward iteration means that we compute z₁, z₂=f(z₁), z₃=f(z₂), etc... Backward iteration means that $z_2=f^{-1}(z_1)$, etc... The solution may be non-unique.

In the first approach (scanline), I nearly always used forward iteration.

To be discussed later, with examples.