Set the co-ordinates of the three corners of a triangle. Take any other pointand plot a pixel midway between it and one of the corners of the triangle chosen at random. Plot another pixel midway between this last pixel and a randomly chosen corner of the triangle. Continue for several thousand pixels.(Ideally discard the first eight points or so).You might expect to see a mess of random points; in fact you get the attractive pattern of a Sierpinskigasket. You may already have a program that does this. If you do not have onejust run"ChaosTrian".
The triangle is not alone in giving patterns - any polygon will do so. If yourun "ChaosSqu" you will get a two-dimensional Cantor set.Here it is necessaryto plot points one third of the way towards a corner of the square. If you plot pixels at halfway points you will get a square apparently filled with random points. This is an illusion as you will see if you run "ChaosSqu2" where pixels have been given different colours depending on the corner of thesquare towards which they are plotted. An alternative, and much faster, method of plotting a two-dimensional Cantor set is given in the recursive program "2DCantor".
Other programs use other polygons having corners from five in the case of "ChaosPenta" up to eight for "ChaosOcta". "ChaosDodec" is thrown in for good measure.
The patterns can be made more complex, and often more attractive, by adding a further point at the centre of the polygon towards which pixels may be randomly attracted. The programs with "Mod" in their names have this extra complexity. The number in the name gives the number of corners of the polygon.
Those of you with a multisynch monitor may find it better to use Mode 18, butmore pixels may well be needed.
