Curlicue Fractal

Choose an irrational number
s
and a horizontal unit segment with angle
ϕ
0
=0
. Define
θ
n+1
=
θ
n
+2πs(mod2π)
, with
θ
0
=0
. To the previous segment, add a new unit segment with angle
ϕ
n+1
=
θ
n
+
ϕ
n
(mod2π)
. The resulting series of line segments is the curlicue fractal. The "temperature" of these fractals measures the boundedness of these curves.

External Links

Curlicue Fractal (Wolfram MathWorld)
Temperature (Wolfram MathWorld)

Permanent Citation

Ed Pegg Jr
​
​"Curlicue Fractal"​
​http://demonstrations.wolfram.com/CurlicueFractal/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007