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Julia set

In complex dynamics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an…

Formal definition, Quadratic polynomials & Equivalent descriptions of the Julia set

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Formal definition

Meromorphic functionRiemann sphereComplexRational functionsComplex polynomials
17 related topics

Quadratic polynomials

Complex quadratic polynomialsMandelbrot setGolden ratioPhotographic mosaicConnected
7 related topics

Equivalent descriptions of the Julia set

ClosurePeriodic pointsEntire functionBoundaryFilled Julia set
5 related topics

Properties of the Julia set and Fatou set

Completely invariant
1 related topics

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Overview

Formal definition

Equivalent descriptions of the Julia set

Properties of the Julia set and Fatou set

Examples

Quadratic polynomials

The potential function and the real iteration number

Field lines

Plotting the Julia set

Bibliography

Advanced semantic analysis

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Map overview Semantic statistics

Julia set

Nodes63
Edges62
Triples137
Avg. degree1.97
Density0.031746
Components1

How this topic connects Entity context

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Julia set

Top relations

related to Bibliography · 41
Julia set → Adrien, Alan, Alexander, Algebra, Annals, Archived, Beardon, Bogomolny, Carleson, Complex Dynamics, Demidov, Douady, DS/9201272, Dynamics, Etude, Evgeny, First, Gamelin, Hubbard, Indexing
related to External links · 41
Julia set → An, April, Archived, Bourke, Burning, Clark University, Crop, David, EMS Press, Encyclopedia, Eric, FractalTS, GNU, Google Labs, Greig, HTML5, HTML5 Fractal, Interactive Julia Set Applet, Iterated Function Systems, Jamie
related to The potential function and the real iteration number · 8
Julia set → As, Fatou, For, Julia, Mandelbrot, The, The Julia, This
is a · 7
Julia set → Cantor space, fractal and not a simple curve, line segment between, point of accumulation for each of the Fatou domains, set of limit points of the full backwards orbit, straight line segment.In other words, unit circle and on this the iteration is given by doubling of angles
related to Using backwards (inverse) iteration (IIM) · 7
Julia set → As, However, Julia, So, Start, That, Unfortunately
related to Plotting the Julia set · 6
Julia set → DEM/J, Distance Estimation Method, IIM, Inverse Iteration Method, Julia, Methods
related to Quadratic polynomials · 6
Julia set → Fix, For, Julia, Mandelbrot, Such, Then
related to Using DEM/J · 6
Julia set → As, Images, It, Julia, Since, Three-dimensional
related to Examples · 5
Julia set → Apart, Fatou, For, Julia, There
related to Equivalent descriptions of the Julia set · 4
Julia set → For, If, Julia, This

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Important terminology

set julia displaystyle fatou iteration function number sets points complex point domain cycle lines mandelbrot operatorname field one two rational

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Julia setis aset of limit points of the full backwards orbit0.90text
Julia setis aunit circle and on this the iteration is given by doubling of angles0.90text
Julia setis aline segment between0.90text
Julia setis afractal and not a simple curve0.90text
Julia setis apoint of accumulation for each of the Fatou domains0.90text
Julia setis aCantor space0.90text
Julia setis astraight line segment.In other words0.90text
Julia setrelated to BibliographyCarleson0.60section
Julia setrelated to BibliographyLennart0.60section
Julia setrelated to BibliographyGamelin0.60section
Julia setrelated to BibliographyTheodore0.60section
Julia setrelated to BibliographyComplex Dynamics0.60section

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