• complex quadratic polynomials
  • planes
  • topology of parameter and dynamical plane
  • Quadratic map
    • Derivatives
    • multiplier ( = eigenvalue )
    • Periodic_points_of_complex_quadratic_mappings
      • Pariodic points for c on horizontal axis
      • Period
    • preperiodic and Misiurewicz points and list of Misiurewicz points
    • critical point, value and orbit
    • Forward and backward ( inverse) iteration
  • dynamics
  • accuracy and computability
  • Dynamic plane , Julia and Fatou sets
    
    • general inf
    • Comparison of various dynamics
    • comparisen of varius radial measure in basin of infinity
    • topological conjugacy:
      • attracting fixed point - hyperbolic dynamics -Koenigs coordinates
      • super attracting fixed point - Bottcher coordinate
      • indiffrent
        • parabolic - Fatou coordinate
        • elliptic -
    • algorithms:
      • IIM
      • BSM
      • DEM/J
      • external angle = arg(phi_c(z))
      • Hubbard-Douady potential = CPM/J = log(phi(z))
      • Equicontinuity
  • Parametr plane and Mandelbrot set for map Fc(z)=z*z + c
    • history
    • definitions
    • Analysis:
    • Algorithms :
      • iterations
      • escape time algorithms:
        • mandelbrot algorithm (boolean test)
        • Level Sets Method for M-set = eLSM/M ( integer)
        • decomposition of exterior of M-set
        • Level Curves method  
        • bailout test
        • Continuus iteration count ( real )
      • Complex potential = Bottcher coordinate = Phi(c) :
        • external angle = arg(phi_m(c))
        • Hubbard-Douady potential = CPM/M = log(phi(c))
        • Jungreis algorithm
          • algorithm
          • list of 2400 coefficients
      • DEM/M =Distance Estimation Method for Mandelbrot set = Milnor algorithm
      • spider algorithm
      • abstract Mandelbrot set
    • Structure of M-set:
      • points and components :
        • Points
        • Sets of points : Components ( periodic orbits )
        • root of component
        • internal addresses
        • boundaries of components
        • centers of components
          • centers and its symbolic sequences for periods 1-10 computed with Maxima bfallroots
          • centers of components computed with eigensolve by Steven Fortune (to do )
          • centers of components computed with MPSolve up to period 14
          • centers of components computed with MPSolve
          • centers of components computed with Maxima command bfallroots from new cpoly.lisp by Raymond Toy and qdynamics
          • centers of components computed with Maxima command allroots
          • centers of components  computed with Maxima package polyroots
            • old version
            • new version (better)
          • centers of components  computed with WEb solver
          • centers of components computed with GNU Octave
          • real centers of components  computed by Jay R. Hill
          • MSS symbolic sequences of centers
        • Number of components
      • angles and rays
        
        • algorithms :
          • Lavaur's algorithm
          • algorithms for finding second angle from pair or parameter rays of root point
        • Internal angle (rotation number) and ray
        • external angle and ray ( = field lines)
          
          • parameter rays for rational angles
            
            • parameter rays of root points
              • parameter rays of root points of period p components
              • parameter rays of root points of components of family F(1/2)
              • parameter rays of root points of mini mandelbrot sets
            • parameter rays of Misiurewicz points
          • parameter rays for irrational angles
        • external and internal parameter rays
      • M-set and Farey sequence
      • Central symmetry
      • questions
    • Programs
    • video
      
• complex cubic polynomials
• Exponential maps
• Limit sets of Kleinian groups
• Newton method
• People
• Dictionary
• Abreviations
• bibliography
  • sources
  • list to get
  • Po polsku ( books in Polish )

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• Programming
  • C
    • Linas C programs
    • Curtis T McMullen - linux programs ( c, bash,perl)
    • Dmitry V. Khmelev  ( look thru WayBack machine
    • C and Dev-c++ and GLUT
  • delphi
  • Lisp
  • Maxima- a free CAS
    • "Mandelbrot" polynomial- computing coefficients of polynomials
    • Lisp and Maxima
  • Gnuplot
  • Octave
  • gimp
  • python
  • The R Project for Statistical Computing
  • MPSolve
    
    • how to run a progam
  • XML
    • MathML
    • test

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• Free programs ( also Open source)
• Linux Mandriva 2007 66-bit on Acer Aspire 9302
• Linux OpenSuse 10.2 64 bit on Acer Aspire 9302

I will appreciate any remark or comment on this site so feel free to e-mail me!

Author: Adam Majewski adammaj1-at-o2-dot-pl

http://fraktal.republika.pl

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