Firstly, you will find none of the “lets make homework cool” type stuff here. The Internet has become a much more stimulating place for maths, visualisation and generative images.
This is in part driven by the death of those “java applets” as wonderful HTML5 based interactive maths content takes glorious hold.

Trying to keep pace with all that is emerging as the new generation of artistic maths geeks put their awesome skills to work.I decided to make this list of the best stuff around.

Google Julia Map:

• “Google maps” for exploring different fractals.
• Allows custom palettes
• Highly interactive
• Lets you share your work.
• here 

Science vs. Magic

• Awesome website that lets you customise and generate many cool things.
• Has animation options.
• Very interactive
• Highly recommend the fractal machine
• http://sciencevsmagic.net/

Mandelbulber

• 3d Fractal rendering
• Free cross-platform software (GNU/GPL)
• Produces stunning results
• Website is here

Rainbow Smoke

• Algorithm by Jozsef Fejes that grew into a media and Internet sensation
• Creates images using one of every RGB24 colour (see our own application for doing this to photos)
• Not interactive, but describes his algorithm, with an early version being downloadable.
  • This means get your coding pants on if you want to mess around with it!
• Website is here

Terragen

• Offering a free version for non-commercial use, terragen has long been an excellent way to generate quality terrains
• Windows / Mac support
• Has a learning curve
• http://planetside.co.uk/

Evolvotron

• Evolve your artistic vision.
• Creation by iteratively choosing what is closest to what you want.
• Great for colourful splashes / wallpapers
• Free and opensource
• Linux only
• Home page is here