Doodle Dandy is a free app that lets you draw in symmetry of 1 (no symmetry), 2 (mirrored), 3, 4, 5, 6, 7, 8, 16, 32 and 64. It has a very simple interface, with only 13 colors and 6 brush thicknesses. No animation or glittering particles. But with this ease of use you can create some stunning spirograph-like kaleidoscopic images, especially with the 64 symmetry and the smallest brush size that resemble colorful crocheted doilies.
I could also have put this in the Kaleidoscopic category too.
It allows you to easily save a 768×1004 image to your photos.