The curlicue fractal is a figure obtained by the following procedure. Let be an irrational number. Begin with a line segment of unit length, which makes an angle to the horizontal. Then define iteratively by

with . To the end of the previous line segment, draw a line segment of unit length which makes an angle

to the horizontal (Pickover 1995ab). The result is a fractal, and the above figures correspond to the curlicue fractals with points for the golden ratio , , , , the Euler-Mascheroni constant , , and the Feigenbaum constant .

The temperature of these curves is given in the following table.

constant	temperature
golden ratio	46
	51
	58
	58
Euler-Mascheroni constant	63
	90
Feigenbaum constant	92