People seem to have a low respect for PostScript, thinking it's just a language used by printers to draw text, lines and the occasional squiggly line, but it is very powerful and quite intelligent. It is a stack based language, beyond being Turing complete, has a large set of curve drawing and mathematical operators. Hmm, sounds like a perfect place to draw math related stuff.

A First Guide to PostScript is a great introduction and PostScript Index has an exhaustive list of functions.

3D Attractors
Lorenz Attractor A representation of fluid dynamics as defined by dx/dt = ρ(y - x), dy/dt = -x z + σx - y, dz/dt = x y - βz
Rössler A model for certain chemical reactions as defined by dx/dt = z - y, dy/dt = x + a y, dz/dt = b + z (x - c).

These are sets of differential equations which are attracted to certain regions and remain bounded by them. They are representations of physical systems.

2D Attractors
Duffing Attractor A representation of a mechanical oscillator as defined by dx/dt = y and dy/dt = x3 - x - αy + f cos(ωt).
Hénon Attractor A mapping defined by (x, y) → (1 + y - αx2, βx).
Lozi Attractor A mapping defined by (x, y) → (1 + y - α|x|, βx).
いけだ (Ikeda) Attractor A mapping defined by (x, y) (1 + u (x cos θ - y sin θ), u (y sin θ + y cos θ)) where θ = 0.4 - 6/(1 + x2 + y2).

These are mappings that are also attracted to certain regions and are bounded.

Matthias Wandel's Transcendental Formula Art
Flower #1 A lotus-like flower.
Flower #2 A daisy-like flower.
Shingles An interlocking scallop pattern.
Slinky A sort of toroidal spring shape.
Waves An undulating sheet pattern.

I stumbled across Matthias Wandel's site and I came across a number of neat looking transcendental formula art, as he termed it, and I have ported them from QuickBasic to PostScript.

Lindenmayer Systems
Arrowhead Curve This an L-system defined by { X Y, F + -, X, X → YF+XF+Y; Y → XF-YF-X } with an angle of 60°.
Dragon Curve This is an L-system defined by { X Y, F + -, FX, X → X+YF+; Y → -FX-Y }.
Hilbert Curve This is an L-system defined by { X Y, F + -, X, X → +YF-XFX-FY+; Y → -XF+YFY+FX- }.
Koch Curve This is an L-system defined by { F + -, F, F → F+F--F+F } with an angle of 60°. It is implemented with similar syntax to rlineto.
Peano Curve This is an L-system defined by { F + -, F, F → F+F-F-F-F+F+F+F-F } . It is implemented with similar syntax to rlineto.
Peano-Gosper Curve This is an L-system defined by { X Y, F + -, X, X → X+YF++YF-FX--FXFX-YF+; Y → -FX+YFYF++YF+FX--FX-Y }.
Penrose Tiling This is an L-system defined by { W X Y Z F, + - [ ], [X]++[X]++[X]++[X]++[X], W → YF++ZF----XF[-YF----WF]++; X → +YF--ZF[---WF--XF]+; Y → -WF++XF[+++YF++ZF]-; Z → --YF++++WF[+ZF++++XF]--XF; F → }.
Sierpinski Gasket This an L-system defined by { X Y, F + -, X, X → --FXF++FXF++FXF--; F → FF } with an angle of 60°.
Square Curve This is an L-system defined by { X, F + -, XF+F+X, X → XF-F+F-XF+F+XF-F+F-X }.

Lindenmayer systems started as a way to model the growth of algae, but now can be used to describe many familiar fractal-like curves, such as the Koch curve and the space-filling Peano curve.

Miscellaneous
ClipStar A toy example to play with fonts and clipping. Produces pretty output.
Fern An itterated function system to draw a fern frond.
Nautilus A nautilus shell drawn using the Fibonacci sequence.

If you are using Windows, you will probably have to get GSView to view these files. If you are lucky enough to be using UN*X, then use GhostScript/GhostView to see these. Or, if you have a PostScript printer, you can feed these files directly to the printer. Don't do that in a public lab! That's just rude!

Neat Things I Didn't Write
Calendar Very nice calendar drawing program.
Draft Watermark For putting DRAFT on the back of pages with extra incentive.
Font Sheets Prints all the fonts available to a printer.
Replace Once resident in a printer's memory, it replace one word for another until the power is cycled.

Links

Other PS Programs
Celtic Knot Thingy A TCL program which generates PS to draw Celtic-style knot work patterns.
Life in PostScript Game of Life in PostScript.
PS HTTPD A web server written in PostScript.
PostScript Fractals A variety of fractals in PostScript.

Documentation
A First Guide to PostScript Very good primer and list of basic commands.
PostScript Index Thorough list of commands.
PostScript Reference Adobe's full PostScript language reference.
Tutorial and Cookbook Nice tutorial and reference.

Software
Adobe Created PostScript and owns the PS Logo.
GSView Windows front-end to GhostScript.
GhostScript Open Source PS interpreter.

If you have some bizarre iterative function, I'd love to try to draw it using PS, not that I can guarantee I can. :-)