University of Granada: Granada, Spain, 2003 pp. In ISAMA-BRIDGES Conference Proceedings Barrallo, J., Friedman, N., Maldonado, J., Martínez-Aroza, J., Sarhangi, R., Séquin, C., Eds. Available online: (accessed on 17 November 2021). In Mathematical Connections in Art, Music and Science, Bridges. Fractal Patterns and Pseudo-tilings Based on Spirals. Einstein’s velocity addition law and its hyperbolic geometry. Hyperbolic geometry: The first 150 years. Direct determination of DNA twist-stretch coupling. Spiral Structure in Galaxies: A Density Wave Theory. Inversion Fractals and Iteration Processes in the Generation of Aesthetic Patterns. Polynomiography for the polynomial infinity norm via Kalantari’s formula and nonstandard iterations. ![]() Frieze and wallpaper chaotic attractors with a polar spin. Beautiful Math: Aesthetic Patterns Based on Logarithmic Spirals. Spiral Patterns of Color Symmetry from Dynamics. Spiral Tilings with Colour Symmetry from Dynamics. Spiral Symmetry World Scientific: Singapore, 1992. The Curves of Life University of Chicago Press: Chicago, IL, USA, 1994. The purpose of this paper is to fill this gap. Due to the attractive aesthetics of spirals and hyperbolic geometry, it is natural to consider the visualization of hyperbolic spiral patterns. However, it seems that no one has attempted to visualize spiral tilings with hyperbolic features. In fact, as an important geometric space, the structure of hyperbolic tilings is well studied see some hyperbolic tilings and Escher-like hyperbolic patterns shown in Figure 2 and Figure 3. Nonetheless, a notable problem is that the study on spiral structures of hyperbolic characteristic is extremely limited people only defined several simple equations of hyperbolic spirals on Poincaré disc see some examples shown in Figure 1. Looking back on history, we clearly see that hyperbolic geometry has become the prelude and preparation for the emergence of relativity in the 20th century. It solved the outstanding parallel postulate problem for two thousand years, which caused a profound revolution in the concept of geometry and space. The hyperbolic geometry founded by Gauss, Bolyai, and Lobachevsky at the end of the 19th century broke the monopoly of Euclidean geometry.
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