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2 2 to the Power of C 2‑fold Embedded Julia Set
3 3‑D 3‑D Rendering 3D
4 4‑fold Embedded Julia Set
A Absolute Value Accuracy Adam Majewski adjacency Adjacency Optimization Adjacency Optimizations Adjacency‑Optimized Adjacent Adjacent Fractions Adrian Douady Aleph‑0 Aleph‑1 Aleph‑2 Algorithm algorithms Aliasing Errors AlmondBread Amygdala Amygdala Index Amygdalan Sects Analytical Naming System Angle angles Antenna antennae Apple Doll Approximation Approximations Area Area History Area of the Mandelbrot Set ART MATRIX ARTMATRIX ARTMATRIX Naming ASCII ASCII Graphics atom Atom Domain atom domains AtomDomain Attractive Component Attractor Automatic Dwell Limit Automatic Math‑Precision
B Ball Ball Arithmetic Beauty of Fractals, the Benoit B. Mandelbrot Benoit Mandelbrot Between Bibliography Bifurcation Bilinear bilinear approximation bilinear interpolation bilinear map Bill Tavis Binary Decomposition Binary Search for Internal Angle bind to binds to bivariate linear Bivariate Linear Approximation Body Boettcher Coordinate Bond bond point bond points bonds Boundary Boundary of the Mandelbrot Set Boundary Scanning Bounded box‑counting Box‑Counting Dimension brain brain medallion Branch Branch Medallion branch medallions Branch Point branch points Brooks and Matelski Brooks‑Matelski Brooks‑Matelski Set Brown Method Bud Buddha Buddhabrot Bug Bulb bulbs Böttcher coordinate
C Cantor Cantor dust Cantor Set Cantor sets Cardioid Cardioid Cusp cardioid cusps cardioids Carrot Cauliflower Cauliflower Medallion cauliflower medallions CC CC\M Cell center Center of Gravity Chaos chaos theory chaotic Child Child Side Children Circle Tiling Claude Heiland‑Allen Cleft Clockwise Cluster Colloquial Colloquial Name Colloquial Names Color Color MANDELZOOM Color Map coloring Common Ancestors Common Smaller Neighbor Common‑Ancestors Method complex Complex Arithmetic complex conjugate complex division complex math Complex Number complex numbers Complex Plane computability Computable Conjugate Connected Connectedness Proof constant Constants Continent Continent Seed Continental Continuous Dwell Continuum continuum hypothesis contour contours coordinate coordinate transform Coordinate Transforms Coordinates Coordinates Used as Names counter‑clockwise Counterclockwise critical Critical Orbit Critical Point Cubic Deltas cubic extrapolation Cusp cusp filaments cusps Cyril Soler
D Decoration decorations Deep deep zoom deep zooming deep zooms Deepest Del‑M Delta Hausdorff Dimension DEM DEM Contours DEM‑Dwell Hybrid DEM/M Dense Derivative Derivative Extrapolation Descendant descendants differential approximation differential estimation diffusion scan Disc Discovery Distance Estimate Distance Estimator Distorted Distortion Dithering diverge DKMANDEL.ARC Douady Rabbit Douady, Adrian double Double Hook Double Precision Double Scepter Valley Double Spiral Double Spiral Medallion double spiral medallions Double Spiral Valley double spirals Double‑Double Down Dr. Mandelbrot Dragon Valley Drawing dust dusts Dwell Dwell Array dwell band Dwell Bands Dwell Limit dwell limits dwells
E East East Valley eastern Easternmost Point eastward Element elements Elephant Elephant Medallion elephant medallions Elephant Valley elephants Elert, Glenn Embedded Julia Set embedded Julia sets embossed Embossed Rendering Encryption Enumeration of Features Equipotential Lines equipotentials Error Diffusion Escape Escape Radius Escape‑Iterations escaped EscapeIterations escapes escaping Ewing and Schober Ewing and Schober paper Ewing, John Exact Coordinates Exploring Exploring the Mandelbrot Set Exponential Map extended double Extended Precision extended‑precision exterior External Angle external angle 1/6 External Angle Plot External Angles External Argument External Arguments external ray external rays ExternalAngle
F Farey Addition Fatou Fatou Dust Fatou dusts Fatou, Pierre Favorite Views 1992 Favorite Views 1993 Favorite Views 1994 Favorite Views 1999 Features Feigenbaum Constant Feigenbaum Point Feigenbaum points Fibonacci Series field line Field Lines Filament filament structure Filament Subset Operator Filament Symmetries Filament Symmetry Filaments First Order Filament first‑order satellite Fixed Point Fixed‑Point Cardioid Fjord Floatexp Floor Floyd's Algorithm Formulas Forstemann, Thorsten forward iteration accuracy FRACT386 fractal Fractal Forge Fractal Foundation Fractal Geometry of Nature, the Fractal Horizons Fractal Witchcraft Fractal, Definition Of Fractal_Geometry_of_Nature fractals FRACTINT Freyman, Ivan Fundamental Dichotomy
G Gaston Julia Glenn Elert Golden Ratio Greg Turk Grid Scan
H Hausdorff Dimension Hausdorff dimensions Head Heiland‑Allen, Claude Hill, Jay History Hook hook Hubbard tree Hubbard trees Hyperbolic Hyperbolic Component hyperbolic components
I Ideal Parameter Selection Imaginary Incremental Dwell Limit Infinite Dwell Limit Infinity influencing island Influencing Mu‑Molecule Inner Neighbor Integer Integer Math Interior Interior Distance Estimate Interior Distance Estimator Interior Dwell Interior of the Mandelbrot Set Internal Address Internal Angle internal angles internal argument Inverse Interpolation Inverse Interpolation for a Quadrilateral Inverse Iteration inverse iteration of Julia sets Inverse Mandelbrot Iteration Inverse‑Iteration Method Inward inwards Island Island Area Survey Island Mu‑Molecule Island Mu‑Molecules Island Mu‑Unit island mu‑units island size estimate Islands iterate iterated Iterates iterating iteration iteration algorithm iterations Ivan Freyman
J Jay Hill Johannes Riedl John Dewey Jones John Dewey Jones midget John Dewey Jones Minibrot John Ewing John Milnor John Stephenson Jonathan Leavitt Jones, John Dewey Jordan Curve Method Jordan Curve Theorem Julia Julia Island Julia islands Julia Medallion Julia Morphing Julia Plane Julia Set Julia sets Julia, Gaston Julia‑Mandelbrot Space Jung Jung Method Jung, Wolf Jung1997Some..Rational
K Kalles Fraktaler Kalles Fraktaler 3 Kevin Martin
L Lake Lakelet Lambda Map larger larger mu‑atom Larger Neighbor Larger Neighbors Largest largest island Largest Islands Largest Mu‑Atoms Laurent Series Lavaurs Algorithm Leavitt Navigation Leavitt, Jonathan Lebesgue measure Left leftmost lemniscate Lemniscates level set Level Sets Lightning Branch Limb Limit Cycle Limit Point Limited‑Region Refinement Line Intersection Lobe lobes Low Dwell Limit Low Resolution
M M macsyma Magnification magnitude Magnitude Main Antenna Main Branch Main Cardioid Main Diagonal Symmetry Main Sequence Majewski, Adam Major Features Mandelbrot Mandelbrot Monk Mandelbrot Set Mandelbrot, Benoit Mandelbrotie Mandelmap Mariani/Silver Mariani/Silver Algorithm Martin, Kevin maxima Maxima maximum dwell Measure Medallion medallions member Member Point Member Points membership Metropolis Metropolis, Nick Metropolis, Stein, and Stein Midget midgets Milnor Milnor, John Milnor1997 Milnor1999Loc Milnor1999Per Minibrot Mirror Symmetries Mirror Symmetry Misiurewicz Misiurewicz Point Misiurewicz points mitochondria Mitochondrion Modified Inverse Iteration Method Modified_IIM Modulus Monte Carlo morphing MSS Algorithm Mu Atom Sizes Mu Map Mu Molecule Symmetries Mu Molecule Symmetry Mu‑atom Mu‑Atom Size Formulas Mu‑atoms Mu‑Ency History Mu‑molecule Mu‑Molecule Metrics Mu‑molecules Mu‑Radical mu‑radicals Mu‑Unit mu‑units MU_01.C Multibrot Set multibrot sets Myrberg Polynomials Myrberg, Pekka Myreberg point
N N‑Fold Embedded Julia Set N‑Max Naming System Naming Systems Needle Needle Medallion needle medallions Neighbor Neighborhood Neighboring Fraction neighboring fractions Neighbors Nested Filament Symmetries Nested Filament Symmetry Net nets Newton's method Newton‑Raphson method Newton‑Raphson Zooming NMAX NN Node nodes Non‑Member Point Non‑Spiral Medallion North North Radical Northeast northern Northernmost Point Northwest nuclei Nucleolus Nucleus
O open conjecture Open Conjectures Optimization Optimizations Optimizations ‑ Domains of Efficacy Orbit Orbit Detection Orbit‑Based Optimization Orbit‑Based Optimizations Orbital Dynamics orbits Order Ordered Dithering Origin Outward outward filament structure outwards Owner
P Palette Paramecia Paramecium Parameter parameter plane Parameter Space Parent Parent Side Patch Iteration Peacock eye peacock‑feather peacock_eyes Peanut peanuts Peitgen Peitgen and Richter Pekka Myrberg Period Period 3 Implies Chaos Period 3 Midget Period 4 Midget Period Detection period domain period domains Period Doubling Period Doubling Bifurcation Period Doubling Bifurcations period doubling cascade Period Scaling period‑3 minibrot period‑4 minibrot periodic periodicity scaling periods perturbation perturbation method Perturbation Methods Phi(N) Pi Pierre Fatou pinwheel Pinwheel Symmetry Pixel Pixel Counting Point points polaftis polar Polar Coordinate System polar coordinates Potential Lines Power MANDELZOOM Power Set Pre‑Periodic Point Precision preperiod preperiodic Primary Primary Filament Primary Filament Operator primary filaments Proboscis Proper Branch Point proper branch points Pseudo‑Code
Q QQ Quad Spiral Valley Quad‑Double Quadratic Quadratic Interpolation Quasi 3‑D Quasi‑Symmetries Quasi‑Symmetry Quaternary
R2 R2 R2 History R2 Name Examples R2 names R2 Naming System R2 Rules R2 Scope R2 System R2‑Name R2.1/2 R2.1/2.1/2 R2.1/2.1/2a R2.1/2.1/3 R2.1/2.1/3a R2.1/2.1/4 R2.1/2.1/4a R2.1/2.1/5 R2.1/2.1/5a R2.1/2.C(1/2) R2.1/2a R2.1/2F(1/3B1)S R2.1/2F(1/5B1)S R2.1/2t R2.1/3 R2.1/3.1/2a R2.1/3.C(1/2) R2.1/3a R2.1/4 R2.1/4a R2.1/5 R2.1/5a R2.2/3 R2.2/3.1/2a R2.2/3a R2.2/5 R2.2/5a R2.2/5F(1/2B1)S R2.3/4 R2.3/4a R2.4/5 R2.4/5a R2.C(0) R2.C(1/2) R2.C(1/3) R2.C(1/4) R2a R2F(1/10B1)S R2F(1/11B1)S R2F(1/2(1/3B1)B) R2F(1/2(1/3B1)B1)S R2F(1/2(2/3B1)B1)S R2F(1/2)B R2F(1/2B) R2F(1/2B1) R2F(1/2B1)FS{2}{2}S R2F(1/2B1)FS{2}FS{2}FS{2}S R2F(1/2B1)FS{2}FS{2}S R2F(1/2B1)FS{2}S R2F(1/2B1)S R2F(1/2B1)S.C(0) R2F(1/2B1)Sa R2F(1/2B1)SF(1/2B1)S R2F(1/2B1){FS{2}}x3S R2F(1/2B1){FS{2}}x4S R2F(1/3B) R2F(1/3B*) R2F(1/3B1) R2F(1/3B1)S R2F(1/3B1)Sa R2F(1/3B2) R2F(1/4B1)S R2F(1/5B1)S R2F(1/6B1)S R2F(1/7B1)S R2F(1/8B1)S R2F(1/9B1)S R2F(14/15B1)S R2F(2/3B1)S R2F(2/5B) R2F(2/5B1)S R2F(2/5B2)S R2F(2/5B3)S R2F(5/8B) R2F(5/8B3)S R2t R2t Series
R Radical Radical Names, AGDP radicals Radius Rank Raster Scan rational coordinate Rational Coordinates Real Real Axis real‑valued dwell recurrence Recurrence Relation recurrence relations Relatively Prime Representation Function representation functions representation methods Resolution Reverse Bifurcation rhop RHOP Algorithm Richard Voss Richter ridge ridge lines Ridgeline ridgelines ridges Riedl Riedl, Johannes Riedl2000 Riemann Sphere Right Robert Devaney Rollo Silver Romera Romera Pastor and Montoya Romera, Miguel Root root point Rotation Number rotation numbers rotational symmetries Rotational Symmetry Roundoff Error RR Runtime Benchmarking
S Satellite Scepter Medallion scepter medallions Scepter Valley Science of Fractal Images, the Scientific American Seahorse Seahorse Medallion seahorse medallions Seahorse Valley Seahorse Valley West Second‑Order Embedded Julia Set Second‑Order Embedded Julia Sets second‑order satellite Secondary secondary continental Secondary Continental Mu‑Atom secondary continental mu‑atoms Secondary Filament secondary filaments Seed Seeds self‑similar self‑similarity Series Approximation Set shepherd crook Shepherds crook Shoulder shoulders Sibling Siblings Siegel Disc Siegel Disk Silver, Rollo Simply Connected simply‑connected single Single Precision Single Spiral Medallion smaller smaller mu‑atom Smaller Neighbor Smaller Neighbors Smallest SMZ Softfloat Soler, Cyril Solid Guessing Solving a System of 2 Equations in 2 Unknowns South South Radical Southeast southern southernmost point Southwest Sparse speed Speed Improvement Speed Improvements Spike Spiral Symmetry spirals Spoke Spokes square root map Square Root Mapping Squaring Stability Window Stephen1991 Stephen1992A Stephen1992B Stephenson Stephenson, John Subset subsets Successive Dwell Limit Successive Refinement successive tradeoff method Successive Tradeoff Methods Successive Tradeoffs method Super MANDELZOOM Superstable Point superstable points Symmetries Symmetry Synchronous Orbit Synchronous‑Orbit Synchronous‑Orbit Algorithm
T Tail Tavis, Bill Tendril Tensor Terminal Point Terminal Points Tertiary The Amygdalan Sects The Beauty of Fractals The Brown Method The Fractal Geometry of Nature the Science of Fractal Images Thorsten Forstemann Thorsten Förstemann three dimensions Tip tips Topknot Tree Triple Spiral Medallion triple spiral medallions Triple Spiral Valley Triple‑Double tuned Tuning Turk, Greg Two‑Dimensional Interpolation
U Up Utter West
V Valley View Virtual Julia Set Virtual Julia Sets Voss, Richard
W West West Radical western westernmost point westward Wolf Jung WWW Interface
X XaoS
Z Zero Plus I ZZ
Recent Additions and Edits to Mu-Ency
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553d 13h ago (2.56K bytes) Embedded Julia Set
553d 13h ago (4.21K bytes) Paramecia
553d 13h ago (825 bytes) R2t Series
551d 9h ago (1.07K bytes) FRACTINT
550d 21h ago (3.29K bytes) Deepest
550d 3h ago (1.96K bytes) Stability Window
550d 3h ago (2.41K bytes) Reverse Bifurcation
549d 23h ago (309 bytes) Synchronous-Orbit Algorithm
549d 20h ago (4.31K bytes) Exponential Map
546d 20h ago (912 bytes) Iterates
546d 19h ago (330 bytes) Misiurewicz Point
546d 19h ago (10.4K bytes) Atom Domain
546d 16h ago (1.30K bytes) Enumeration of Features
545d 6h ago (4.68K bytes) Floatexp
545d 6h ago (2.76K bytes) Ball Arithmetic
544d 14h ago (439 bytes) Largest Islands
544d 8h ago (556 bytes) Island Area Survey
543d 16h ago (2.57K bytes) Bivariate Linear Approximation
543d 16h ago (5.46K bytes) External Angle
543d 15h ago (882 bytes) Heiland-Allen, Claude
543d 15h ago (564 bytes) Kalles Fraktaler
539d 6h ago (574 bytes) Amygdala
538d 12h ago (1.21K bytes) Feigenbaum Point
537d 9h ago (1.13K bytes) John Dewey Jones Minibrot
517d 3h ago (818 bytes) Bibliography
505d 8h ago (5.44K bytes) Successive Refinement
505d 7h ago (1.12K bytes) Leavitt Navigation
505d 7h ago (4.90K bytes) Amygdala Index
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