A number of programs can be used to create moirè images, op art, illusions and textures. If you have one you like you can message me on Facebook and I'll consider adding it to the list.
One of my favorite programs is Filter Forge. Filter Forge is both a stand-alone application and a high-end plugin for Adobe Photoshop that gives you the power to create your own filters without any programming knowledge at all. Filters include seamless textures, visual effects, distortions, patterns, backgrounds, frames, and more.
Kaleider manipulates images to emulate various Kaleidoscope, Mirroring, 3D Mirroring and Funneling effects. It is a capable graphics tool for people who are interested in symmetry, tiling, tessellation and mosaic patterns, with controls for manipulating images and tiles.
This is a cool nice little program for making Magic Eye type stereograms.
I use a number of programs within the Adobe Suite. Photoshop and Illustrator being the primary ones for images. I also use Dreamweaver, Acrobat and inDesign. I'm looking at learning After Effects.
Although Adobe makes some wonderful products I must admit I generally despise Adobe. Their products have become buggy and their customer service has always sucked. Adobe has bought up several other companies I used products from and then killed them off. Their subscription model I'm sure is good for their shareholders, but as a customer I hate them for it.
For the type of work I do, I need hem, but if you don't I'd avoid them. Software that costs you as theirs does much year after year should be reliable.
Much like gimp or Photoshop Affinity Photo allows you to manipulate images. It's priced nicer than Adobe, but is not yet as full-fledged. It does run much faster though and seems much more reliable at this time.
I plan on expanding this list in the future to include other programs, to include ones I don't personally use. If you know of a great program of this type you can message me on Facebook.