Various fractals

What are fractals? A fractal is a geometric figure in which a similar motive is repeated on a smaller scale. (H. Lauwerier)

A fractal can be regarded as a colour graph, comparable with maps in an atlas. In an atlas mountain ranges are brown; the higher the range the darker brown its colour. Shallow seawater is light blue, deep-sea water is darker blue, etc.

A similar thing goes for fractals. Each point in the plane is examined for a particular quality. On the basis of this examination the point gets a particular colour. In this way we get marvelous diagrams. The sort of examination is defined by the type of fractal.

A small selection of my collection is shown underneath.
The fractal is made by means of Fractint (Iterated Function Systems (IFS)). Such an IFS is a function of the plane on itself with the help of calculation of probability.
A Lyapunov fractal.
A fractal type lambda, made by my fractal-mate Dick Berents
A magnificent fractal from a demo-set of Fractint.
Type fn(z)+fn(pix) using the functions cotan and sqr.
A part from the Mandelbrot-set.
This fractal started the popularity of fractals, all thanks to Benoit. B. Mandelbrot. Born in Warsaw in 1924 he left for Paris in 1936. In 1958 he went to the USA. He worked among other things at IBM and as a professor at Harvard University. Thanks to the computer we can now make graphics of fractals.
What a beautiful picture a simple equation like z8=1 can produce.
This fractal is one of the Newton type.
A nice example of self-similarity. With a little imagination one can see two footsteps. In each step you see two small steps and in those small ones smaller ones again, etc.
A fine composition taken from a CD-ROM
Another fractal of the lambda type, made in bygone days