Papers Related to Mathematics and Art

The following papers, arranged in reverse chronological order, are available as pdf downloads.

Iterating Polyominoes to Create Fractal Reptiles, Robert W. Fathauer, Proceedings of Bridges 2025: Mathematics and the Arts (2025), pages xx-xx.

Ceramic-based Mixed Media Topological Sculpture, Robert W. Fathauer, Proceedings of Bridges 2024: Mathematics, Music, Art, Architecture, Culture (2024), pages xx-xx.

Ceramic Bells: Aural Performance and Geometric Design, Robert W. Fathauer, Proceedings of Bridges 2023: Mathematics, Music, Art, Architecture, Culture (2023), pages 283-290.

Crested Cactuses and Mathematical Sculpture, Robert W. Fathauer, Proceedings of Bridges 2022: Mathematics, Music, Art, Architecture, Culture (2022), pages 111-118.

Logarithmic Spiral Tilings of Triangles, Robert W. Fathauer, Proceedings of Bridges 2021: Mathematics, Music, Art, Architecture, Culture (2021), pages 55-62.

A Method for Creating Dendritic Fractal Tiles, Robert W. Fathauer, Proceedings of Bridges 2020: Mathematics, Music, Art, Architecture, Culture (2020), pages 49-56.

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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