The boolean stream Q is defined by

Q = 1:f(Q)

for the stream function f defined by

f(0:s) = 1:0:f(s)

f(1:s) = 0:0:1:f(s)

This stream shows up a remarkable balance between regular and chaotic behavior

Below you find a few turtle visualizations all of this single stream Q. More precisely, a number N and two angles a0 and a1 are specified, and then elements of the stream are traversed: if the symbol 0 is read then the drawing direction is moved a0 degrees to the right; if the symbol 1 is read then the drawing direction is moved a1 degrees to the left. In both cases after doing so a line of unit length is drawn. This is repeated N times. Initially the color is mainly red. This color changes smoothly until it is blue at the end. In the mean time the green part of the color varies.

N = 200,000, a0 = a1 = 118

N = 200,000, a0 = a1 = 48

N = 100,000, a0 = a1 =100

N = 32,000, a0 = a1 = 113

N = 130,000, a0 = a1 = 114

N = 80,000, a0 = a1 = 79

N = 200,000, a0 = 36, a1 = 88

N = 200,000, a0 = 158, a1 = 197

N = 140,000, a0 = 33, a1 = 88