The Curlicue Fractal is defined as follows:
Choose an irrational number $s$ and a horizontal unit segment with angle $\phi_0 = 0$. Define $\theta_{n+1} = \theta_{n} + 2 \pi s \pmod{2 \pi}$, with $\theta_0=0$. To the previous segment, add a new unit segment with angle $\phi_{n+1} = \theta_{n} + \phi_{n} \pmod{2 \pi}$. The resulting series of line segments is the curlicue fractal. The "temperature" of these fractals measures the boundedness of these curves.
$s = e\times\gamma$ creates a very high temperature for this fractal, far greater than all the millions of other irrational numbers I've tried. Does any other irrational number beat it?