The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group

Algorithm 1

CreatingWallpaperPattern()// algorithm for creating patterns with the wallpaper symmetry.

BEGIN

start x = 0

end x = .1415926

start y = 0

end y = .1415926//Set pi = 3.1415926

step x = (end x – start x)/X res//Xres is the resolution in X direction

step y = (end y – start y)/Y res//Yres is the resolution in Y direction

FOR i = 0 TO X res DO

FOR j = 0 TO Y res DO

x = start x + i   step x

y = start y + j   step y

FOR k = 1 TO MaxIter//MaxIter is the number of iterations, the default set is 100

/Given a invariant mapping associated with a wallpaper group as iteration

function and initial point (x, y), function Iteration (x, y) iterates MaxIter times. The iterated

sequences are stored in the array Sequence/.

Sequence = Iteration (x, y)

END FOR

/Inputting Sequence, the color scheme OrbitTrap outputs the color /

= OrbitTrap (Sequence)

Set color to point (x, y)

END FOR

END FOR

END