Fractal Lab

Bibliography

References

The canonical books, foundational papers, and tooling cited across Fractal Lab.

Canonical books

  1. The Fractal Geometry of NatureBenoît B. Mandelbrot, W. H. Freeman, 1982.
  2. Fractal Geometry: Mathematical Foundations and ApplicationsKenneth Falconer, Wiley, 3rd ed., 2014.
  3. Fractals EverywhereMichael F. Barnsley, Academic Press, 2nd ed., 1993.
  4. The Science of Fractal ImagesHeinz-Otto Peitgen and Dietmar Saupe (eds.), Springer, 1988.
  5. Chaos and Fractals: New Frontiers of SciencePeitgen, Jürgens, Saupe, Springer, 2nd ed., 2004.
  6. Measure, Topology, and Fractal GeometryGerald A. Edgar, Springer, 2nd ed., 2008.
  7. An Introduction to Chaotic Dynamical SystemsRobert L. Devaney, Westview, 2nd ed., 2003.

Landmark papers

  1. How long is the coast of Britain? Statistical self-similarity and fractional dimensionB. Mandelbrot, Science, 1967.
  2. Fractal aspects of the iteration of z ↦ λz(1−z) for complex λ and zB. Mandelbrot, Annals of the New York Academy of Sciences, 1980.
  3. On the dynamics of polynomial-like mappingsAdrien Douady and John H. Hubbard, Ann. Sci. ENS, 1985.
  4. The Hausdorff dimension of the boundary of the Mandelbrot set and Julia setsMitsuhiro Shishikura, Annals of Mathematics, 1998.
  5. Mémoire sur l'itération des fonctions rationnellesGaston Julia, J. Math. Pures Appl., 1918.
  6. Sur les équations fonctionnellesPierre Fatou, Bull. Soc. Math. France, 1919-1920.
  7. Fractals and Self SimilarityJohn E. Hutchinson, Indiana Univ. Math. J., 1981 (foundational IFS theorem).

Originating works on classical fractals

  1. Über unendliche, lineare PunktmannigfaltigkeitenGeorg Cantor, Mathematische Annalen, 1883 (Cantor set).
  2. Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaireHelge von Koch, Arkiv för Matematik, 1904 (Koch curve).
  3. Sur une courbe dont tout point est un point de ramificationWacław Sierpiński, Comptes Rendus, 1915 (Sierpinski triangle).
  4. Allgemeine Räume und Cartesische Räume. Teil IIKarl Menger, 1926 (Menger sponge / universal 1D space).

Online & tooling

  1. Wikipedia: FractalCross-linked overview.
  2. Wikipedia: List of fractals by Hausdorff dimensionReference table.
  3. Paul Bourke's fractals pageLong-running resource with deep coverage.
  4. Inigo Quilez (iquilezles.org)Distance-estimated raymarching and shader fractals.
  5. ShadertoyVast community library of fractal shaders.