Yet another
recipe for making a
fractal at home. This one will require the use of an
eraser, or the
background colour. (See
Sierpinski triangle for other ingredients.) This one, however, will be
deterministic.
Take a straight line. Divide it into three equal parts. Draw an equilateral triangle using the central part as the base of the triangle. Erase the base of the triangle. You now have something which looks (roughly) like this: _/\_ Now do what you did to your original line to every straight line in the figure. Iterate.
In L-system and turtle graphics terms, this might be written as a system with {f,l,r} as the alphabet (interpreting `f' as forward, `l' as turning left 60 degrees, `r' as turning right 60 degrees), f -> flfrrflf as the only rule, and `frrfrrfrr' as the initial string.
You can always start with an equilateral triangle in the first place, in which case the second generation of the iterated function system will be a star of David.
The Koch snowflake is an example of a space-filling curve.