A number of programs can be used to create moirè images, op art, illusions and textures. These a just some I have used over the years.
I use several programs within the Adobe Suite. Photoshop and Illustrator being the primary ones for images. I also use Dreamweaver, Acrobat, and InDesign. I’m also exploring After Effects. Adobe makes excellent products, but I find their software increasingly buggy, and their customer service is consistently poor.
Adobe has acquired and then discontinued several products I previously used. Their subscription model might be good for shareholders, but as a customer, I find it frustrating. For my work, these tools are necessary, but if you don’t need them, I would suggest looking for alternatives due to the cost and reliability issues.
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.
filterforge.com
This is a cool nice little program for making Magic Eye type stereograms.
I use both for these free programs for 3d Renders.
Great programs for playing around with math. Geogebra is free to use and has an online and downloadable version. Excel is part of the Microsoft Office Suite.
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.