Fractals and Mathematical Art

Fractals & mathematical art bring mathematics alive in a visually appealing way! Well-known examples are the Mandelbrot Set, and Harmonographs (popularised in science museums as devices drawing intricate curves on paper). Here’s a list of resources for you to discover more about these fascinating pictures - and how you can make your own!

About Fractals & Mathematical Art

  1. 1 Fractal 25
  2. 2 Fractal art 21
  3. 3 Fractals, Chaos, Self Similarity 14
  4. 4 An Introduction to Fractals 15
  5. 5 Fractal forums 7
  6. 6 Mandrian's Mandelbrot Music (title picture) 7
  7. 7 Fractal Art l Facebook Group 0

Fractal Geometry

  1. 1 Introduction to Fractal Geometry 8
  2. 2 the sierpinski triangle page to end most sierpinski triangle pages 13
  3. 3 Representing and modelling geometry in SecondLife 5
  4. 4 Fractal Geometry 10
  5. 5 Sierpinski Gasket (title picture) 5

The Mandelbrot Set

  1. 1 Mandelbrot set 15
  2. 2 Fractals/Iterations in the complex plane/Mandelbrot set 4
  3. 3 Mandelbrot fraktaler super deep 2 2^4750 8
  4. 4 Mandelbrot Set -- from Wolfram MathWorld 3
  5. 5 Mercator Mandelbrot Maps 6
  6. 6 Understanding the mandelbrot set 1
  7. 7 Mandel zoom 01 head and shoulder (title picture) 0

Menger Sponge

Frost Patterns

A Julia Set

The Buddhabrot

  1. 1 Large Buddhabrot 19
  2. 2 Buddhabrot 21
  3. 3 Buddhabrot (moleculardensity.net) 8
  4. 4 The Buddhabrot fractal rendering method 8
  5. 5 Buddhabrot Fractals 11
  6. 6 Buddhabrot, Mu-Ency at MROB 2
  7. 7 - YouTube 8
  8. 8 moleculardensity 10

Fractals in Nature

  1. 1 Earth's Most Stunning Natural Fractal Patterns 40
  2. 2 Natural phenomena with fractal features 6
  3. 3 Google Earth Fractals 8
  4. 4 Fractals in Nature 5

Julia Sets

  1. 1 Filled Julia Set 5
  2. 2 The Julia and Mandelbrot Sets 4
  3. 3 Fractals/Iterations in the complex plane/Julia set 1
  4. 4 Julia set 2
  5. 5 Julia Set -- from Wolfram MathWorld 0
  6. 6 Julia Sets 1

Nebulabrot (Buddhabrot)

3D Fractals

  1. 1 METAFRACTALS 19
  2. 2 Building 3D Fractals 16
  3. 3 Hypercomplex Fractals 7
  4. 4 Mandelbulb 2
  5. 5 Mandelbulb.com 1
  6. 6 Mandelbulber :: 0
  7. 7 The Unravelling of the Real 3D Mandelbrot Fractal 5
  8. 8 Incendia 0

Spectral Harmonograph

M. C. Escher

  1. 1 M. C. Escher 8
  2. 2 Google Search 0
  3. 3 M.C. Escher 3
  4. 4 470 artworks 3
  5. 5 Tessellations 11
  6. 6 M.C. Escher Documentary (by CINEMEDIA-NPS-RNTV) [1999] 1
  7. 7 MC Escher, Images of Mathematics... 2
  8. 8 The Mathematical Art Of M.C. Escher 1

Escher Circle Limit III by M.C.Escher

The Harmonograph

  1. 1 Harmonograph 10
  2. 2 Harmonograph 10
  3. 3 Harmonograph -- from Wolfram MathWorld 6
  4. 4 Harmonograph 5
  5. 5 Virtual Harmonograph 12
  6. 6 Walking Randomly 5
  7. 7 Black & White Harmonographs 0
  8. 8 Online 3D Harmonograph 0

Starship Mandelbrot

Fractal Art Galleries

  1. 1 35 Phenomenal Fractal Art Pictures 13
  2. 2 40 Amazing 3D Fractals Using Apophysis 7
  3. 3 52 Amazing Fractal Art Images With Rich Colors 7
  4. 4 The Largest Online Art Gallery and Community 1
  5. 5 Fractal World Gallery 6
  6. 6 ker2x's buddhabrot gallery 5
  7. 7 Gallery of Computation 2
  8. 8 Amazing Seattle Fractals 4

Mandelbulb

Fractal Software

  1. 1 Ultra Fractal 15
  2. 2 Jwildfire 4
  3. 3 GNU XaoS 6
  4. 4 Apophysis 3
  5. 5 Electric Sheep 3
  6. 6 Fractalnow 6
  7. 7 Frax 7
  8. 8 Gnofract 4D 7

Elliptic Alien Egg

Mathematical & Algorithmic Art

  1. 1 Algorithmic art 19
  2. 2 Algorithmic Mathematical Art 17
  3. 3 The Mathematical Art of M.C. Escher 6
  4. 4 Mathematical imagery by Jos Leys. 8
  5. 5 Math Artwork 14
  6. 6 The Beauty of Roots 11
  7. 7 The beauty of mathematics 9
  8. 8 Mathematical Masterpieces 2

Code for Programmers

  1. 1 Mandelbrot image in every language 12
  2. 2 Mandelbrot set 24
  3. 3 Fractal tree 10
  4. 4 Sierpinski carpet 4
  5. 5 Sierpinski triangle 9
  6. 6 Sierpinski triangle/Graphical 4
  7. 7 Dragon curve 7
  8. 8 Popular Python recipes tagged "fractal" 6

Benoit B Mandelbrot

Why is geometry often described as “cold” and “dry?” One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

― Benoît B. Mandelbrot

Picture Attributions

  1. 1 Mandelbrot Set 5
  2. 2 Menger Sponge 2
  3. 3 Julia Set 4
  4. 4 Frost Patterns 3
  5. 5 Nebulabrot (Buddhabrot) 1
  6. 6 Mandelbulb 2
  7. 7 Escher Circle Limit III 3
  8. 8 Spectral Harmonograph 1

How Amazing is That?

Both the Mandelbrot & the Julia sets are generated by computing z*z+c and feeding back the result as the next value of z. z & c are so-called ‘complex numbers’, which aren’t complicated at all. It simply means that they are composed of 2 parts, ‘real’ and ‘imaginary’, like so: z=x+iy, where i*i=-1. The feedback loop is stopped either when z exceeds some value, or the loop has repeated more than some number of times. Which one happens determines if the point being tested is inside or outside the set. If outside, the size of z may be used to pick a colour for the point. Infinite complexity from a few lines of code - how amazing is that?

Miscellaneous

  1. 1 “Rudy Set” as Ultimate Cubic Mandelbrot Set. Quartics & Quintics, too! 11
  2. 2 Hidden Dimension Galleries 6
  3. 3 Algebraic Surfaces Gallery 2
  4. 4 Fractal Curves 0

Hypershapes

  1. 1 Imgur 11
  2. 2 r/hypershape 7
  3. 3 Hyper-Shapes (Slices of 4D Objects) 6

Space-Filling Curves

  1. 1 Space-filling curve 2
  2. 2 Hilbert Curves 3
  3. 3 Pandimensional Space-Filling Curves 3
  4. 4 Plane Filling Curves 2
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