(The programs in this directory may be freely copied providing that it is not for profit and that all the files including this one are kept together.)
Most people would be very happy to have just one or two space-filling
curves named after them, e.g. Gosper, Hilbert and Peano. However, Yoshio
Ohno and Koichi Ohyama have published a whole catalogue of symmetric self-
similar space-filling curves in the Journal of Recreational Mathematics,
Vol.23, pp161-174, 1991. In that paper they draw the generators of their
curves and I have used a simple L-System program to enable the full fractal
curves to be plotted on an Archimedes.
In general the generators are very complex having up to 49 steps. Those basedon a square grid start with an "S" and those on a triangular grid start with
a "T". The number indicates the steps in the generator and a lower case
letter is used to distinguish between otherwise similar curves. (The curve
T7a2 is in fact the same as the Gosper fractal).
In most cases I have provided two versions of the fractals. Those ending in
the number "2" have a lower depth of recursion giving a rapid plot that showsthe structure of the curve, while those without a "2" have a higher depth of recursion, take longer to plot and demonstrate the space-filling nature of