Math in Art

John Golden

finding mathematics in artworks. Some attempt at sorting, first by artists, when there was a specific model, then some recurring mathematical structures. See also a GeoGebra book of tessellations, [url]https://www.geogebra.org/m/CUdKaHeC[/url], and Islamic geometry, [url]https://www.geogebra.org/m/wh3gyeEN[/url].

Table of Contents

  1. Albers
    1. Albers-StructuralConstellation12.2
    2. Albers-Structural Constellation12.1
    3. Albers-StructuralConstellation12.3
    4. Albers Tectonic
    5. Albers Co-ordinal
    6. Albers Dilations
    7. Albers Make Your Own Constellation
  2. Bill
    1. max bill Pythagorean Squares
    2. Max Bill System
    3. Rotating Nested Regular Polygons
  3. Herrera
    1. After Carmen Herrera
    2. Herrera Square
  4. Kandinsky
    1. À la Kandinsky - Art by Transformations
    2. Kandinsky Generator
    3. Kandinsky Box
  5. Klee
    1. Thresholds, after Paul Klee
    2. After Klee - Variations
  6. LeParc
    1. After Le Parc
    2. Alchimie after LeParc
  7. Lewitt
    1. After Sol Lewitt
  8. Lohse
    1. Lohse Square
    2. Lohse Serial
  9. Mangold
    1. Mangold Ellipse
    2. Mangold Circles
  10. Mondrian
    1. After Mondrian
    2. Générateur de Mondrian
    3. Waar was Mondriaan echt mee bezig?
  11. Hélio Oiticica
    1. Hélio Oiticica
    2. Hélio Oiticica
    3. Helio Oiticica Proportions
  12. Riley
    1. Bridget Riley Bands
    2. Bridget Riley - Turn
    3. Fragment, Bridget Riley
    4. Bridget Riley Blaze
    5. Bridget Riley, La Lune
    6. Riley's Arrest
    7. Reverse
    8. Composition with Circles
    9. Riley Rectangles
  13. Stella
    1. Hyena Stomp - Frank Stella
    2. Mambo Variations on Frank Stella
  14. Vasarely
    1. Vasarely Doors
    2. Vasserely Squares
    3. Vasarely Dots
    4. Vasarely and homothety
    5. Stack of Squares
    6. Vasarely Epsylon
    7. Vasarely Ellipses 1
    8. Vasarely Ellipses 2
    9. Vasarely Hexes
    10. Vasarely Lacerta
  15. Other Artists
    1. Anita NH Squares
    2. Anuszkiewicz Inflexion
    3. Apollonio Disk
    4. Barns-Graham Squares
    5. Geraldo de Barros
    6. Caixas 1
    7. Carvão Quadrilateral
    8. Carvão 2018
    9. Dadamaino Lines
    10. Decrauzat Sines
    11. Escher Conformal Grid
    12. Fleming Grid
    13. Edmund's Circles
    14. Isermann Square
    15. Loewensberg Stack
    16. Longuet Labyrinth
    17. Semicircles (a la Eduardo MacEntyre)
    18. Five Circles
    19. Maymont Assembly
    20. Nilson Triangles
    21. Optica Squares
    22. Helga Phillips' Circles
    23. Regolo's Torus
    24. Keith Richardson-Jones Drawing
    25. Luiz Sacilotto
    26. Schleifer Turning
    27. Shonk's Reinvention
    28. Leon Polk Smith Circles
    29. Sobrino Sectors
    30. Suggs Polygons
    31. Hervé Tullet Game
    32. Visser Shift
    33. Lines - Joy Walker
    34. Wiegand Spiral
    35. González Bogen Flag
    36. Landis Grid
  16. Fractals
    1. Fractal Tree
    2. Parallelogram Pile
    3. Star Fractal by Justin Lanier
    4. Fractal Tiling
    5. Something nerdy
  17. Impossible
    1. Impossible triangle hexagons
    2. Impossible Box
  18. IGP
    1. Qarawiyyin Mosque
    2. An Alhambra Tessellation
    3. Qarawiyyin Tiling (generalized)
  19. Perspective
    1. Two towels on a beach—an application of Desargues's theorem
    2. Algebra of Perspective
    3. Perspective
  20. Polygons
    1. Round About
    2. Polygon Portals
    3. Polygon Pop Art
    4. N N-gons
    5. PolyRing
    6. Nested Polygons
    7. Lauand Triangles
    8. Spiraling Quadrilaterals
    9. Turning Hexes
    10. Transmogrify
    11. Polygonal Line Art
    12. Right Angle Rosette
  21. Quadrilaterals
    1. A Pleasant Arrangement of Rectangles
    2. Fathauer Kites
    3. Quad Cycle
    4. Similar Quadrilaterals
    5. Tolerance
    6. Rhombus Stars
    7. Mosaics
    8. Kite Spiral
    9. Stacks
  22. Randomly Generated
    1. Random Trees
    2. Four Ways
    3. Two ways
    4. Cool pattern
    5. Egyptian Triangles
    6. Optical Inequality
    7. Hitomezahi Stitching
    8. Tauba Auerbach Dot Dash
    9. Vera Molnar Grid
    10. Semaphore
  23. Spirals
    1. Polygonal Path
    2. Pythagorean Spiral
    3. Dot Disc
    4. Ilonka Squares
    5. Polygonal Spiral
    6. Triangle Spiral
    7. Not Spiral
  24. String Art
    1. Curved String Art
    2. String Art
    3. strings into circles-circles tangents.
    4. Harmonic Lineart
    5. Circle Line Drawings
    6. Parametric String Art
    7. Bertoia Rectangles
    8. Square String Functions
    9. Polygon Catcher
    10. Polygon Catcher - Rectangle
    11. Spiky Feathers
    12. Superficie reglada de Jack Eagan
  25. Tessellations
    1. Cat Tiling
    2. Escherized Pentagon Tessellation
    3. Double Glide Reflection Tessellation
    4. Yemeni Squares
    5. Hexagonal Fish
    6. Dilated Tessellation
    7. Cubicles
  26. Tiles
    1. Fatis Tiles
    2. Octagon Truchet
    3. Infinity Tiles
    4. Truchex Mix
    5. Puzzolo Squares
    6. Truchet Squares
    7. Triangle Truchet
    8. Argyle Dominoes
  27. Triangles
    1. A Fibonacci Triangle
    2. Triangle Divisions
    3. Golden Triangles
    4. Infinite Integer Triangles
    5. Triangle Stars
  28. Other Math Structures
    1. Fibonacci Circles
    2. the golden ratio (and aphrodite's phi)
    3. Grid Deformations
    4. H Symmetry
    5. Manhole
    6. Moiré Patterns
    7. Mosaic Art II
    8. Mosaics: Ellipses
    9. Octangularity
    10. Box Quilt
    11. Truchet Quilt
    12. Rays
    13. Rosassa D6 de la Catedral - versió I
    14. Sequential Circles
    15. Spin Planes
    16. Stars and Garters
    17. Straight Line Mandala
    18. Star Slinky
    19. Weaving
    20. Yin Yang Weave
    21. Zig Zag
    22. Venn Moiré
    23. Tool for Exploring Color Palettes

1.

Albers

  • 1. Albers-StructuralConstellation12.2
  • 2. Albers-Structural Constellation12.1
  • 3. Albers-StructuralConstellation12.3
  • 4. Albers Tectonic
  • 5. Albers Co-ordinal
  • 6. Albers Dilations
  • 7. Albers Make Your Own Constellation

1.1.

–

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

2.

Bill

  • 1. max bill Pythagorean Squares
  • 2. Max Bill System
  • 3. Rotating Nested Regular Polygons

2.1.

–

2.2.

–

2.3.

–

3.

Herrera

  • 1. After Carmen Herrera
  • 2. Herrera Square

3.1.

–

3.2.

–

4.

Kandinsky

  • 1. À la Kandinsky - Art by Transformations
  • 2. Kandinsky Generator
  • 3. Kandinsky Box

4.1.

–

4.2.

–

4.3.

–

5.

Klee

  • 1. Thresholds, after Paul Klee
  • 2. After Klee - Variations

5.1.

–

5.2.

–

6.

LeParc

Julio LeParc

  • 1. After Le Parc
  • 2. Alchimie after LeParc

6.1.

–

6.2.

–

7.

Lewitt

  • 1. After Sol Lewitt

7.1.

–

8.

Lohse

  • 1. Lohse Square
  • 2. Lohse Serial

8.1.

–

8.2.

–

9.

Mangold

Robert Mangold

  • 1. Mangold Ellipse
  • 2. Mangold Circles

9.1.

–

9.2.

–

10.

Mondrian

  • 1. After Mondrian
  • 2. Générateur de Mondrian
  • 3. Waar was Mondriaan echt mee bezig?

10.1.

–

10.2.

–

10.3.

–

11.

Hélio Oiticica

  • 1. Hélio Oiticica
  • 2. Hélio Oiticica
  • 3. Helio Oiticica Proportions

11.1.

–

11.2.

–

11.3.

–

12.

Riley

  • 1. Bridget Riley Bands
  • 2. Bridget Riley - Turn
  • 3. Fragment, Bridget Riley
  • 4. Bridget Riley Blaze
  • 5. Bridget Riley, La Lune
  • 6. Riley's Arrest
  • 7. Reverse
  • 8. Composition with Circles
  • 9. Riley Rectangles

12.1.

–

12.2.

–

12.3.

–

12.4.

–

12.5.

–

12.6.

–

12.7.

–

12.8.

–

12.9.

–

13.

Stella

  • 1. Hyena Stomp - Frank Stella
  • 2. Mambo Variations on Frank Stella

13.1.

–

13.2.

–

14.

Vasarely

  • 1. Vasarely Doors
  • 2. Vasserely Squares
  • 3. Vasarely Dots
  • 4. Vasarely and homothety
  • 5. Stack of Squares
  • 6. Vasarely Epsylon
  • 7. Vasarely Ellipses 1
  • 8. Vasarely Ellipses 2
  • 9. Vasarely Hexes
  • 10. Vasarely Lacerta

14.1.

–

14.2.

–

14.3.

–

14.4.

–

14.5.

–

14.6.

–

14.7.

–

14.8.

–

14.9.

–

14.10.

–

15.

Other Artists

  • 1. Anita NH Squares
  • 2. Anuszkiewicz Inflexion
  • 3. Apollonio Disk
  • 4. Barns-Graham Squares
  • 5. Geraldo de Barros
  • 6. Caixas 1
  • 7. Carvão Quadrilateral
  • 8. Carvão 2018
  • 9. Dadamaino Lines
  • 10. Decrauzat Sines
  • 11. Escher Conformal Grid
  • 12. Fleming Grid
  • 13. Edmund's Circles
  • 14. Isermann Square
  • 15. Loewensberg Stack
  • 16. Longuet Labyrinth
  • 17. Semicircles (a la Eduardo MacEntyre)
  • 18. Five Circles
  • 19. Maymont Assembly
  • 20. Nilson Triangles
  • 21. Optica Squares
  • 22. Helga Phillips' Circles
  • 23. Regolo's Torus
  • 24. Keith Richardson-Jones Drawing
  • 25. Luiz Sacilotto
  • 26. Schleifer Turning
  • 27. Shonk's Reinvention
  • 28. Leon Polk Smith Circles
  • 29. Sobrino Sectors
  • 30. Suggs Polygons
  • 31. Hervé Tullet Game
  • 32. Visser Shift
  • 33. Lines - Joy Walker
  • 34. Wiegand Spiral
  • 35. González Bogen Flag
  • 36. Landis Grid

15.1.

–

15.2.

–

15.3.

–

15.4.

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15.5.

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15.6.

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15.7.

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15.8.

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15.9.

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15.10.

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15.11.

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15.12.

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15.13.

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15.14.

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15.15.

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15.16.

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15.17.

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15.18.

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15.19.

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15.20.

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15.21.

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15.22.

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15.23.

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15.24.

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15.25.

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15.26.

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15.27.

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15.28.

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15.29.

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15.30.

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15.31.

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15.32.

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15.33.

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15.34.

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15.35.

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15.36.

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16.

Fractals

  • 1. Fractal Tree
  • 2. Parallelogram Pile
  • 3. Star Fractal by Justin Lanier
  • 4. Fractal Tiling
  • 5. Something nerdy

16.1.

–

16.2.

–

16.3.

–

16.4.

–

16.5.

–

17.

Impossible

Forced perspective

  • 1. Impossible triangle hexagons
  • 2. Impossible Box

17.1.

–

17.2.

–

18.

IGP

Islamic geometry

  • 1. Qarawiyyin Mosque
  • 2. An Alhambra Tessellation
  • 3. Qarawiyyin Tiling (generalized)

18.1.

–

18.2.

–

18.3.

–

19.

Perspective

  • 1. Two towels on a beach—an application of Desargues's theorem
  • 2. Algebra of Perspective
  • 3. Perspective

19.1.

–

19.2.

–

19.3.

–

20.

Polygons

  • 1. Round About
  • 2. Polygon Portals
  • 3. Polygon Pop Art
  • 4. N N-gons
  • 5. PolyRing
  • 6. Nested Polygons
  • 7. Lauand Triangles
  • 8. Spiraling Quadrilaterals
  • 9. Turning Hexes
  • 10. Transmogrify
  • 11. Polygonal Line Art
  • 12. Right Angle Rosette

20.1.

–

20.2.

–

20.3.

–

20.4.

–

20.5.

–

20.6.

–

20.7.

–

20.8.

–

20.9.

–

20.10.

–

20.11.

–

20.12.

–

21.

Quadrilaterals

  • 1. A Pleasant Arrangement of Rectangles
  • 2. Fathauer Kites
  • 3. Quad Cycle
  • 4. Similar Quadrilaterals
  • 5. Tolerance
  • 6. Rhombus Stars
  • 7. Mosaics
  • 8. Kite Spiral
  • 9. Stacks

21.1.

–

21.2.

–

21.3.

–

21.4.

–

21.5.

–

21.6.

–

21.7.

–

21.8.

–

21.9.

–

22.

Randomly Generated

  • 1. Random Trees
  • 2. Four Ways
  • 3. Two ways
  • 4. Cool pattern
  • 5. Egyptian Triangles
  • 6. Optical Inequality
  • 7. Hitomezahi Stitching
  • 8. Tauba Auerbach Dot Dash
  • 9. Vera Molnar Grid
  • 10. Semaphore

22.1.

–

22.2.

–

22.3.

–

22.4.

–

22.5.

–

22.6.

–

22.7.

–

22.8.

–

22.9.

–

22.10.

–

23.

Spirals

  • 1. Polygonal Path
  • 2. Pythagorean Spiral
  • 3. Dot Disc
  • 4. Ilonka Squares
  • 5. Polygonal Spiral
  • 6. Triangle Spiral
  • 7. Not Spiral

23.1.

–

23.2.

–

23.3.

–

23.4.

–

23.5.

–

23.6.

–

23.7.

–

24.

String Art

  • 1. Curved String Art
  • 2. String Art
  • 3. strings into circles-circles tangents.
  • 4. Harmonic Lineart
  • 5. Circle Line Drawings
  • 6. Parametric String Art
  • 7. Bertoia Rectangles
  • 8. Square String Functions
  • 9. Polygon Catcher
  • 10. Polygon Catcher - Rectangle
  • 11. Spiky Feathers
  • 12. Superficie reglada de Jack Eagan

24.1.

–

24.2.

–

24.3.

–

24.4.

–

24.5.

–

24.6.

–

24.7.

–

24.8.

–

24.9.

–

24.10.

–

24.11.

–

24.12.

–

25.

Tessellations

  • 1. Cat Tiling
  • 2. Escherized Pentagon Tessellation
  • 3. Double Glide Reflection Tessellation
  • 4. Yemeni Squares
  • 5. Hexagonal Fish
  • 6. Dilated Tessellation
  • 7. Cubicles

25.1.

–

25.2.

–

25.3.

–

25.4.

–

25.5.

–

25.6.

–

25.7.

–

26.

Tiles

  • 1. Fatis Tiles
  • 2. Octagon Truchet
  • 3. Infinity Tiles
  • 4. Truchex Mix
  • 5. Puzzolo Squares
  • 6. Truchet Squares
  • 7. Triangle Truchet
  • 8. Argyle Dominoes

26.1.

–

26.2.

–

26.3.

–

26.4.

–

26.5.

–

26.6.

–

26.7.

–

26.8.

–

27.

Triangles

  • 1. A Fibonacci Triangle
  • 2. Triangle Divisions
  • 3. Golden Triangles
  • 4. Infinite Integer Triangles
  • 5. Triangle Stars

27.1.

–

27.2.

–

27.3.

–

27.4.

–

27.5.

–

28.

Other Math Structures

  • 1. Fibonacci Circles
  • 2. the golden ratio (and aphrodite's phi)
  • 3. Grid Deformations
  • 4. H Symmetry
  • 5. Manhole
  • 6. Moiré Patterns
  • 7. Mosaic Art II
  • 8. Mosaics: Ellipses
  • 9. Octangularity
  • 10. Box Quilt
  • 11. Truchet Quilt
  • 12. Rays
  • 13. Rosassa D6 de la Catedral - versió I
  • 14. Sequential Circles
  • 15. Spin Planes
  • 16. Stars and Garters
  • 17. Straight Line Mandala
  • 18. Star Slinky
  • 19. Weaving
  • 20. Yin Yang Weave
  • 21. Zig Zag
  • 22. Venn Moiré
  • 23. Tool for Exploring Color Palettes

28.1.

–

28.2.

–

28.3.

–

28.4.

–

28.5.

–

28.6.

–

28.7.

–

28.8.

–

28.9.

–

28.10.

–

28.11.

–

28.12.

–

28.13.

–

28.14.

–

28.15.

–

28.16.

–

28.17.

–

28.18.

–

28.19.

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28.20.

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28.21.

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28.22.

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28.23.

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Information