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CommonsEdit

log-polar mappingEdit

other imagesEdit

other JuliaEdit

  • θ = 1/(10 + 1/(10 + · · ·)) Consider a polynomial P : C → C of degree d ≥ 2, with an irrationnally indifferent fixed point at the origin: P(0) = 0, P′ (0) = e 2iπθ, θ ∈ R \ Q.

( from On the linearization of degree three polynomials and Douady’s conjecture by Arnaud Ch´eritat (joint work with Xavier Buff)

cubicEdit

  • A 4k cubic Julia by ‎Chris Thomasson‎ . Here is the formula: z = pow(z, 3) - (pow(-z, 2.00001) - 1.0008875);

Julia sets for fc(z) = z*z + cEdit

0.3305 + 0.06i[1]

0.253930 + 0.000480i.

0.27310 + 0.006990i.

Julia set c=0.763069-0.094691i

−0.200062 + 0.807120i.

http://yozh.org/2011/03/14/mset006/

0.3-0.49i

-0.75 -0.1i ; ( outside Mandelbrot set ) -0.7589-0.0753i http://social-biz.org/2010/03/28/generating-chaos/

const double Cx=-0.74543; const double Cy=0.11301;

-0.808 +0.174i;

-0.1 +0.651i; ( beween 1 and 3 period component of Mandelbrot set )

-0.294 +0.634i

San Marco Fractal = Basilica : c = - 3/4


disconnectedEdit

3 petalsEdit

C= -0.125 +0.649519 i

Siegel DiskEdit

Julia set = Jordan curve Irrational recurrent cycles

  • 0.59...+i0.43...
  • 0.33...+i0.07...
  • C= -0.408792866 -0.577405 i
  • c=-0.390541-0.586788i

OtherEdit

Feigenbaum: C= -1.4011552 +0.0 i

Tower: C= -1 + 0.0 i

Cauliflower: C= 0.25 +0.0 i


DendriteEdit

Critical point eventually periodic 0 > -2 > 2 (fixed).

C= i

c^3 + 2c^2 +2c +2 =0

OtherEdit

Circle: C= 0.0 +0.0 i

Segment: C= -2 +0.0 i

centersEdit

  • (0.355534, -0.337292) it is a center of period 85 componnet. Adress 1->5 -> 85, by ‎Chris Thomasson‎
  • 29 cycle power of two Julia set by ‎Chris Thomasson‎ at point: (-0.742466, -0.107902) address 1 -> 29
  • 38-cycle power of 3 Julia at point (0.388823, -0.000381453) I discovered:
  • c = -0.051707765779845 +0.683880135777732 i period = 273, 1 -(1/3)-> 3 -(1/7)-> 21 -(1/13)-> 273 https://www.math.stonybrook.edu/~jack/tune-b.pdf
  • https://arxiv.org/pdf/math/9411238.pdf see Figure.2
    • 1- (1/3) → 3 -(2/3) → 7
    • 1 - (1/2) -> 2 - (1/2) → 4 -(1/3) → 7
    • 1-(1/3) → 3- (1/2) → 4
    • 1-(1/3) → 3 - (1/2) → 5-(1/2) → 6
    • 1-(1/3) → 3-(1/2) → 5-(1/2) → 7
    • 1-(1/3) → 3-(1/3) → 7
  • http://wrap.warwick.ac.uk/35776/1/WRAP_THESIS_Sharland_2010.pdf

minibrot=Edit

  • c = 0.284912968784722 +0.484816779093857 i period = 84


Superattracting per 3 (up to complex conjugate)Edit

C= -1.75488 (airplane)

C= -0.122561 + 0.744862 i (rabbit) Douady's Rabbit Rabbit: C= -0.122561 +0.744862 i = ( -1/8+3/4 i ??? ) whose critical point 0 is on a periodic orbit of length 3


Superattracting per 4 (up to complex conjugate)Edit

C= -1.9408

C= -1.3107

C= -1.62541

C= -0.15652 +1.03225 i

C= 0.282271 +0.530061 i


KokopelliEdit

  • p = γM (3/15)
  • p(z) = z^2 0.156 + 1.302*i
  • The angle 3/15 or p0011 has preperiod = 0 and period = 4.
  • The conjugate angle is 4/15 or p0100 .
  • The kneading sequence is AAB* and the internal address is 1-3-4 .
  • The corresponding parameter rays are landing at the root of a primitive component of period 4.
  • c = -0.156520166833755 +1.032247108922832 i period = 4


Superattracting per 5 (up to complex conjugate)Edit

C= -1.98542

C= -1.86078

C= -1.62541

C= -1.25637 +0.380321 i

C= -0.50434 +0.562766 i

C= -0.198042 +1.10027 i

C= -0.0442124 +0.986581 i

C= 0.359259 +0.642514 i

C= 0.379514 +0.334932 i

A superattracting per 15Edit

C= -0.0384261 +0.985494 i

denseEdit

Density near the cardoid 3 by DinkydauSet Mandelbrot set

Again a location that's not deep but super dense.

Magnification: 2^35.769 5.8552024369543422761426995117521 E10

Coordinates: Re = 0.360999615968828800 Im = -0.121129382033034400

aEdit

https://plus.google.com/u/0/photos/115452635610736407329/albums/6124078542095960129/6124078748270945650 frond tail Misiurewicz point of the period-27 bulb of the quintic Mandelbrot set (I don't have a number ATM, but you can find that)

Machine-readable_dataEdit

ADAM MAJEWSKI development

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Bezier curveEdit

psEdit

"Obrazy w indywidualnym wkładzie, mam z samodzielnie napisanymi programami PASCAL (FREEPASCAL) i / lub XFIG (program do rysowania pod LINUX) początkowo tworzone jako pliki EPS. Niestety bezpośrednia integracja plików EPS z Wikipedią nie jest możliwa. Przydatna jest konwersja plików EPS na pliki XFIG za pomocą PSTOEDIT. Konwersja plików EPS na pliki SVG jest możliwa dzięki INKSCAPE, a także eksportowi plików xfig do plików SVG. Jednak nie znalazłem zamiennika dla etykiety LATEX, włączając ją do pliku LATEX w środowisku rysunkowym z plikiem psfrag. Także dla licznych możliwości manipulowania krzywymi za pomocą xfig wiem w inkscape (wciąż) brak odpowiednika. Z plików PS tworzę pliki SVG z ps2pdf i pdf2svg i używam programu inkscape do dostosowania stron (marginesów) do rysunków." de:Benutzer:Ag2gaeh

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       Mathematical Function Plot
Description Function displaying a cusp at (0,1)
Equation  
Co-ordinate System Cartesian
X Range -4 .. 4
Y Range -0 .. 3
Derivative  
 
Points of Interest in this Range
Minima  
Cusps  
Derivatives at Cusp  ,

 

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