Papers Related to Fractals, Knots, and Tiling

The following papers are available as pdf downloads. Clicking on the title will take you to the paper's page in the Bridges Archive, which shows the abstract and includes a link to download the full paper. They are arranged below in reverse chronological order.

A Method for Creating Dendritic Fractal Tiles, Robert W. Fathauer, to be published in Proceedings of Bridges 2020: Mathematics, Music, Art, Architecture, Culture (2020).

Walkable Curves and Knots, Robert W. Fathauer, Proceedings of Bridges 2019: Mathematics, Music, Art, Architecture, Culture (2019), pages 13-20.

Art and Recreational Math Based on Kite-Tiling Rosettes, Robert W. Fathauer, Proceedings of Bridges 2018: Mathematics, Music, Art, Architecture, Culture (2018), Pages 15-22.

Fractal Gaskets: Reptiles, Hamiltonian Cycles, and Spatial Development, Robert W. Fathauer, Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Culture (2016), Pages 217-224.

Some Hyperbolic Fractal Tilings, Robert W. Fathauer, Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014), Pages 87-94.

Aesthetic Patterns Based on Fractal Tilings, Peichang Ouyang and Robert W. Fathauer, IEEE Computer Graphics and Applications, Pages 6-14 (2014).

Iterative Arrangements of Polyhedra - Relationships to Classical Fractals and Haüy Constructions, Robert W. Fathauer, Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013), Pages 175-182.

Two-color Fractal Tilings, Robert W. Fathauer, Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012), Pages 199-206.

Photographic Fractal Trees, Robert W. Fathauer, Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011), Pages 105-112.

Some Three-dimensional Self-similar Knots, Robert W. Fathauer, Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010), Pages 103-110.

Fractal Tilings Based on Dissections of Polyominoes, Polyhexes, and Polyiamonds, Robert W. Fathauer, Homage to a Pied Piper, edited by Ed Pegg, Jr., Alan H. Schoen, and Tom Rogers, A.K. Peters, Wellesley, MA, pp. 145-158 (2009).

A New Method for Designing Iterated Knots, Robert W. Fathauer, Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009), Pages 251-258.

A Fractal Crystal Comprised of Cubes and Some Related Fractal Arrangements of other Platonic Solids, Robert W. Fathauer, Hank Kaczmarski and and Nicholas Duchnowski Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture (2008), Pages 289-296.

Fractal Knots Created by Iterative Substitution, Robert W. Fathauer, Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007), Pages 335-342.

Fractal Tilings Based on Dissections of Polyominoes, Robert W. Fathauer, Bridges London: Mathematics, Music, Art, Architecture, Culture (2006), Pages 293-300.

Fractal Tilings Based on Dissections of Polyhexes, Robert W. Fathauer, Renaissance Banff: Mathematics, Music, Art, Culture (2005), Pages 427-434.

Fractal Patterns and Pseudo-tilings Based on Spirals, Robert W. Fathauer, Bridges: Mathematical Connections in Art, Music, and Science (2004), Pages 203-210.

Graphical Fractals Based on Circles - Abstract, Robert W. Fathauer, Bridges: Mathematical Connections in Art, Music, and Science (2002), Page 305.

Fractal tilings based on v-shaped prototiles, Robert W. Fathauer, Computers and Graphics, Vol. 26, pp. 635-643 (2002).

Fractal tilings based on kite- and dart-shaped prototiles, Robert W. Fathauer, Computers and Graphics, Vol. 25, pp. 323-331 (2001).

Self-similar Tilings Based on Prototiles Constructed from Segments of Regular Polygons, Robert W. Fathauer, Bridges: Mathematical Connections in Art, Music, and Science (2000), Pages 285-292

Extending Escher's Recognizable-Motif Tilings to Multiple-Solution Tilings and Fractal Tilings, Robert W. Fathauer, M.C. Escher's Legacy - A Centennial Celebration, edited by Doris Schattschneider and Michele Emmer, Springer, pp. 154-165 (2002).

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Fractal Tiling Fractal Knots Gasket Fractals Fractal Trees Hyperbolic & Folded Fractals Polyhedra Papers etc.