Curlicue Fractal
The curlicue fractal is a figure obtained by the following procedure. Let 
be an Irrational Number. Begin with aline 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 1995). The result is a Fractal, and the above figures correspond to the curlicue fractalswith 10,000 points for the Golden Ratio
, 
, 
, 
, the Euler-Mascheroni Constant 
,
, and 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 |
References
Berry, M. and Goldberg, J. ``Renormalization of Curlicues.'' Nonlinearity 1, 1-26, 1988. Moore, R. and van der Poorten, A. ``On the Thermodynamics of Curves and Other Curlicues.'' McQuarie Univ. Math. Rep. 89-0031, April 1989. Pickover, C. A. ``The Fractal Golden Curlicue is Cool.'' Ch. 21 in Keys to Infinity. New York: W. H. Freeman, pp. 163-167, 1995. Pickover, C. A. Mazes for the Mind: Computers and the Unexpected. New York: St. Martin's Press, 1993. Sedgewick, R. Algorithms in C, 3rd ed. Reading, MA: Addison-Wesley, 1998. Stewart, I. Another Fine Math You've Got Me Into.... New York: W. H. Freeman, 1992.
- Epstein Zeta Function
- Equal
- Equal by Definition
- Equal Detour Point
- Equality
- Equally Likely Outcomes Distribution
- Equal Parallelians Point
- Equiaffinity
- Equiangular Spiral
- Equianharmonic Case
- Equi-Brocard Center
- Equichordal Point
- Equichordal Problem
- Equidecomposable
- Equidistance Postulate
- Equidistant Cylindrical Projection
- Equidistributed Sequence
- Equilateral Hyperbola
- Equilateral Triangle
- Equilibrium Point
- Equilic Quadrilateral
- Equinumerous
- Equipollent
- Equipotent
- Equipotential Curve