Comment by userbinator
9 years ago
The pair of equations can be expressed succinctly as
y -= x >> 4;
x += y >> 4;
and is basically a very rough approximation of a step in the CORDIC[1] algorithm, which computes the sin and cos of an angle by rotating a vector; it's then quite natural that successive rotations would trace out an approximation to a circle.
As such, many of the first programs of the PDP-1 were “Display hacks”: Programs using only a few lines of code, but when run, create intricate patterns on the screen.
The demoscene has carried on that tradition, and in particular the sub-512b categories produce very interesting graphics from tiny programs.
and this formula is simply an expression of the fact that given a circle:
x = sin t , y = cos t
the derivative is
d(sin t) = (cos t) dt , d(cos t) = -(sin t) st
so it's interesting that it was "stumbled" upon.