Another famous one is Fractint . The following venture into the Mandelbrot set was done using Tierazon. Zooming in produces picture 2. The process is shown repeated up to picture 6 but could have continued indefinitely. Repeating patterns are what you might expect from something generated by a repetitive process, and that is what you will see.
Self similarity is a common feature of fractals and nature, a classic example being the fern.
If you break a branch off you still have an almost identical, but smaller, fern. Tierazon can very quickly generate pictures like the following examples which often look similar to images found in the natural world. As each picture element is found by lots of repeated calculations, the faster your computer works the better. Tierazon has the option of different working formulae and lots of filters and colouring options. If you have plenty of disc space you can make animated zooms or movement.