Mandelbrot set explorer

Mandelbrot Set for map F(Z)=Z*Z + C

It is a program for drawing mandelrot set for function F(c,z)=z*z + c
It uses diffrent algorithms ( see below) and color types (program works in pf32bit color mode = True Color. Other modes are simulated)
It is made with Borland Delphi

source code with exe files

Features:

it uses only CPU for computing

relatively high speed due to: ScanLine Procedure and cardioid checking;

Zoom - clickin the image can magnify (left) or diminish (right) picture

saving the image as bmp file and txt file describing the image - click on the image below to see this file.

dialog boxes to change the parameters: Bitmap, C plane, Algorithm

it uses standard Borland Delphi = VCL units

uses extended type of floating point numbers

one can draw one image on another ( something like layers - see checkbox in AlgorithmDlg)

one can choose parameter plane by 4 corners or by center and 2 sides (C_PlaneDlg )

one can check period of hyperbolic component of interior of Mandelbrot set in status bar and see the hyperbolic components (color is proportional to period)

diffrent target sets for escape time iteration ( old versions only)

draw the equipotential curves

in psedo8bit color mode opens fractint palette files = *.map

big version of components = 2000 x 2000 pixels = 15 MB

To do :

*Jungreis algotithm
*spider algorithm
* interactively recompute julia set when changing by a mouse/cursor pad the c parameter
* plot out the itineraries of arbitrary points
* find out the periodic points of the point with a given period
* for a given point compute (interactively) its coordinates, and the derivetiev of several iterated of the function in thath point
* Approximate localization of the tip and the root of a given nervure
* show the external or internal rays in any periodic component of Fatou and Mandelbrot set
* display the argument of any ray and allow to iterate the function upon that external ray
* computing the address of any point in Julia set / Mandelbrot set

Credits:

cardioid checking is based on code of Hugh Allen program Mandel / Julia Explorer

rainbow gradient : Function Rainbow by Witold J.Janik

clickin the image can magnify (left) or diminish (right) - it i based on code by Tomasz TSD Dzierkowski c64.nostalgia.pl ( inactive link)

periodicity checking is based on program MANCHAOS.BAS written in PowerBASIC by J. C. Sprott

level curves method for escape time algorithm is translations of BASIC program of M. Romera

My version of Milnor algorithm = DEM/M is translation ( with modification) of :

algorithm published by Robert P. Munafo

Mandelbrot Dazibao program in QBasic

true color images are based on Evgeny Demidov version

Robert P. Munafo :
"The Distance Estimator method was pioneered by Thurston, and was made known to the general community by Peitgen and Richter in their book The Beauty Of Fractals. The actual algorithm is presented in The Science Of Fractal Images, page 198 (Peitgen and Saupe, editors)."

Hubbard-Douady potential of Mandelbrot set =CPM/M is based on the code by Inigo Quilez

Procedures ( old or wrong) :

Draws only M-set in black and white exterior pf8bit

Bad procedures for drawingf Arg(Phi(c)) = External angle of Mandelbrot set

Main page
Autor: Adam Majewski
Feel free to e-mail me. (:-)) adammaj1-at-o2-dot--pl

Strona utworzona przy pomocy programu: EditPlus www.editplus.com
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