"Generative art" software which evolves images/textures/patterns through an iterative process of random mutation and user-selection driven evolution. If you like lava lamps, and still think the Mandelbrot set is cool, this could be the software for you.
Taprats is a Java applet that implements an islamic tiling technique based on the work of Hankin in the early part of the twentieth century, and on more recent papers by A.J. Lee and Craig S. Kaplan. By Craig S. Kaplan and Pierre Baillargeon.
There is a new version rewritten for Windows under the name Alhambra. See here: https://github.com/pierrebai/Alhambra/releases
Knotter is a highly configurable interlace designer.
Interlace patterns are a kind of design historically used as a decorations in many places and by different cultures, some examples are Celtic knotworks and Islamic interlaces.
Knotter aims to allow its user to design such patterns in an intuitive way and to provide easy ways to integrate the result in external general-purpose graphic software.