Nova Fractal - Formula

Formula

The formula for the Nova fractal is a generalization of a Newton fractal:

where is said to be a relaxation constant and . If c = 0, this expression reduces to the Newton fractal formula:

for . Usually, is assigned the value 3, while is an adjustable parameter, and is the location variable, for a "Mandelbrot Nova".

Fractals
Characteristics
  • Fractal dimension (Hausdorff dimension & Topological dimension)
  • Self-similarity
  • Recursion
Iterated function system
  • Koch snowflake
  • Cantor set
  • Sierpinski carpet
  • Sierpinski triangle
  • Space-filling curve
  • Dragon curve
  • T-square
  • Menger sponge
  • Barnsley fern
Strange attractor
  • Multifractal system
L-system
  • Space-filling curve
Escape-time fractals
  • Mandelbrot set
  • Julia set
  • Burning Ship fractal
  • Nova fractal
  • Lyapunov fractal
Random fractals
  • Lévy flight
  • Percolation theory
  • Self-avoiding walk
  • Fractal landscape
  • Brownian motion
  • Brownian tree
  • Diffusion-limited aggregation
People
  • Georg Cantor
  • Felix Hausdorff
  • Gaston Julia
  • Paul Lévy
  • Aleksandr Lyapunov
  • Benoit Mandelbrot
  • Lewis Fry Richardson
  • Wacław Sierpiński
  • Helge von Koch
Other
  • List of fractals by Hausdorff dimension
  • "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension"

Read more about this topic:  Nova Fractal

Famous quotes containing the word formula:

    “Every formula which expresses a law of nature is a hymn of praise to God.”
    —Maria Mitchell (1818–1889)

    “But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the formula for that? The formula for that is not included in the curriculum.”
    —Fannie Hurst (1889–1968)

    “Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
    —Pierre Simon De Laplace (1749–1827)