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.
- Legendre Function of the Second Kind
- Legendre-Gauss Quadrature
- Legendre-Jacobi Elliptic Integral
- Legendre Polynomial
- Legendre Polynomial of the Second Kind
- Legendre Quadrature
- Legendre Relation
- Legendre's Chi-Function
- Legendre's Constant
- Legendre Series
- Legendre's Factorization Method
- Legendre's Formula
- Legendre's Quadratic Reciprocity Law
- Legendre Sum
- Legendre Symbol
- Legendre Transformation
- Lehmer Method
- Lehmer Number
- Lehmer-Schur Method
- Lehmer's Constant
- Lehmer's Formula
- Lehmer's Phenomenon
- Lehmer's Problem
- Lehmer's Theorem
- Lehmus' Theorem