|
gptkbp:instanceOf
|
mathematical set
|
|
gptkbp:application
|
gptkb:data_visualization
chaos theory
computer art
|
|
gptkbp:borders
|
fractal
|
|
gptkbp:compact
|
true
|
|
gptkbp:definedIn
|
gptkb:complex_plane
|
|
gptkbp:dimensions
|
2
|
|
gptkbp:discoveredBy
|
gptkb:Benoit_Mandelbrot
|
|
gptkbp:field
|
fractal geometry
complex dynamics
|
|
gptkbp:firstDescribed
|
1980
|
|
gptkbp:hasApplication
|
computer graphics
education
mathematical modeling
|
|
gptkbp:hasArea
|
finite
|
|
gptkbp:hasBoundaryPoints
|
uncountably infinite
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasEquation
|
z_{n+1} = z_n^2 + c
|
|
gptkbp:hasExterior
|
true
|
|
gptkbp:hasFractalDimension
|
2
|
|
gptkbp:hasHausdorffDimension
|
2
|
|
gptkbp:hasInfinitePerimeter
|
true
|
|
gptkbp:hasLebesgueMeasure
|
positive
|
|
gptkbp:hasNoSymmetry
|
about imaginary axis
about origin
|
|
gptkbp:hasSubgroup
|
antennae
bulbs
main cardioid
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Mandelbrot set
|
|
gptkbp:influenced
|
gptkb:fractal_art
popular mathematics
|
|
gptkbp:interiorFeatures
|
true
|
|
gptkbp:isBounded
|
true
|
|
gptkbp:isClosed
|
true
|
|
gptkbp:isNotDifferentiable
|
true
|
|
gptkbp:isNotPathConnected
|
false
|
|
gptkbp:isNotSmooth
|
true
|
|
gptkbp:isPathConnected
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:location
|
gptkb:complex_plane
|
|
gptkbp:namedAfter
|
gptkb:Benoit_Mandelbrot
|
|
gptkbp:property
|
self-similarity
connected set
fractal boundary
|
|
gptkbp:relatedTo
|
gptkb:Julia_set
|
|
gptkbp:studiedIn
|
gptkb:mathematics
complex analysis
dynamical systems
fractal geometry
|
|
gptkbp:symmetry
|
about real axis
|
|
gptkbp:variant
|
c (complex number)
z (complex number)
|
|
gptkbp:visualizationColoring
|
escape time algorithm
|
|
gptkbp:visualizes
|
computer graphics
|
|
gptkbp:bfsParent
|
gptkb:Dynamical_Systems
gptkb:Yoccoz_puzzles
gptkb:Mandelbrot
|
|
gptkbp:bfsLayer
|
5
|