Abstract
By a stretch of imagination we shall identify spirals with systems of interacting particles. Mimicking the formalism of Statistical Mechanics we shall then discover that spirals go through a phase transition as the “temperature” increases. The inverse critical temperature coincides with the box dimension of the spiral. The article is a restatement of previous joint work [1].
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References
Y. Dupain, M. Mendes France, C. Tricot. Dimensions des spirales, Bull. Soc. Math. Fr. 111, (1983),193–201.
H. Steinhaus. Sur la portée pratique et théorique de quelque théoréms sur la measure des ensembles de drotes, Comptes rendus du ler congrés des Mathématiciens des pays Slaves, (1930), 353–354.
H. Steinhaus. Length, Shape and Area, Colloquium Mathematicum, 3, (1954), 1–13.
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© 1995 Plenum Press, New York
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Dupain, Y., France, M.M., Tricot, C. (1995). Spirals and Phase Transitions. In: Takahashi, Y. (eds) Algorithms, Fractals, and Dynamics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0321-3_4
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DOI: https://doi.org/10.1007/978-1-4613-0321-3_4
Publisher Name: Springer, Boston, MA
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