fractal_explorer.m

Fractal Explorer GUI-based program for exploring and studying the most common form of fractals, c

function varargout = fractal_explorer(varargin)
% FRACTAL_EXPLORER - Chaos, Lindenmayer Systems, Strange Attractors and
% more...
%
% CSE Fractal Explorer is a GUI-based program for exploring and studying the
% most common form of fractals, chaotic systems and fractional dimension systems.
% An overview of the features with a small introductory text is available at
% http://ltcmail.ethz.ch/cavin/fractals.html
%
% The usage is strightforward. Type "fractal_explorer", and the main window
% will be opened and the Mandelbrot Set will be drawn. All features are available
% via menus and buttons. Information is given on the bottom-left corner of the
% figure, while tips and information will appear on the left side of the figure
% when user input is required/possible.
%
% The features include:
% - Logistic Equation [1]
% - Real 2D Attractors:
%     - Henon Attractor [1]
%     - Pickover System [1]
%     - Arbitrary Quadratic Map [1]
% - Real 3D Attractors:
%     - Lorenz Attractor [2]
%     - Roessler Attractor [2]
%     - Limited Quadratic Map [2]
% - Complex Maps:
%     - Mandelbrot Set [1,5]
%     - Julia Sets [1,3,5]
%     - Arbitrary Polynomial Newton-Raphson Attraction Basins [1,5]
%     - Barnsley's Tree [1,5]
%     - Arbitrary Mandelbrot and Julia-based Sets [1,5]
% - Quaterions:
%     - Mandelbrot and Julia Sets [2]
% - String Systems:
%     - Lindemayer Systems Single Rule
%     - Lindenmayer Systems Multiple-Rules
%     - Plant-like systems:
%         - Barbsley's Fern [4,6]
%         - Fractal Trees
%     - 3D Systems
%         - 3D-Multiple-Rules Lindenmayer Systems [2]
%         - Menger Sponge [2,4]
% - Folded Plans:
%     - Mesh grids [2]
%     - Fractals Clouds
%     - Fractal Landscapes [2]
% 
% Notes:
% [1] Interactive Zooming
% [2] Interactive 3-D View
% [3] Julia explorer with on-the-fly previews
% [4] Limited to built-in parameters
% [5] Include the function Make-It-3D!
% [6] Equations taken from Brian Mearns's "Fractal Fern"
%     http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=4372&objectType=file
% 
% For most functions, dialogs will allow introducing user-defined parameters or 
% equations for the calculation. Most dialog contains a button labeled "Cool Params" -
% this will propose a set of parameters leading to a chaotic behavior (as it is
% sometimes difficult to find a good parameter set); when only one "good" set of
% parameter is known, it will be given by default the first time the function is called.
%
% Written by L.Cavin, 30.07.2004, (c) CSE
% This code is free to use and modify for non-commercial purposes.
% Web address: http://ltcmail.ethz.ch/cavin/fractals.html#SOFT

% FOLLOWS THE STANDARD GUIDE COMMENTS:
%
% FRACTAL_EXPLORER M-file for fractal_explorer.fig
%      FRACTAL_EXPLORER, by itself, creates a new FRACTAL_EXPLORER or raises the existing
%      singleton*.
%
%      H = FRACTAL_EXPLORER returns the handle to a new FRACTAL_EXPLORER or the handle to
%      the existing singleton*.
%
%      FRACTAL_EXPLORER('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in FRACTAL_EXPLORER.M with the given input arguments.
%
%      FRACTAL_EXPLORER('Property','Value',...) creates a new FRACTAL_EXPLORER or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before fractal_explorer_OpeningFunction gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to fractal_explorer_OpeningFcn via varargin.
%
%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one
%      instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help fractal_explorer

% Last Modified by GUIDE v2.5 28-Jul-2004 15:29:22

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @fractal_explorer_OpeningFcn, ...
                   'gui_OutputFcn',  @fractal_explorer_OutputFcn, ...
                   'gui_LayoutFcn',  @fractal_explorer_LayoutFcn, ...
                   'gui_Callback',   []);
if nargin & isstr(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT


% --- Executes just before fractal_explorer is made visible.
function fractal_explorer_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to fractal_explorer (see VARARGIN)

% Choose default command line output for fractal_explorer
if nargin > 3
    disp('unknown input arguments:');
    varargin{:}
end

handles.output = hObject;

axes(handles.main_axis);
gridsize = get(handles.main_axis, 'position');
handles.gridsize = gridsize(3);
handles.space = get_mandelbrot_initial(handles.gridsize);
handles.main_image = image(handles.space);
axis(handles.main_axis, 'off');

% CANCELLING INACTIVE MENU ITEMS
set(handles.menu_rabinovich, 'Enable', 'off');

handles.xmin = -2;
handles.xmax = 1;
handles.ymin = -1.5;
handles.ymax = 1.5;
handles.itern = 70;
handles.mode = 1; % mandelbrot
handles.xjul = 0;
handles.yjul = 0;

handles = fillupdescription(handles);

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes fractal_explorer wait for user response (see UIRESUME)
% uiwait(handles.fractal_explorer);


% --- Outputs from this function are returned to the command line.
function varargout = fractal_explorer_OutputFcn(hObject, eventdata, handles)
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;


% --- Executes on button press in button_cancel.
function button_cancel_Callback(hObject, eventdata, handles)
% hObject    handle to button_cancel (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

set(handles.button_3D, 'Enable', 'on');
delete(handles.preview_image);
set(handles.txt_zoom_1, 'Visible', 'off');
set(handles.txt_zoom_2, 'Visible', 'off');
set(handles.button_cancel, 'Visible', 'off');
set(handles.button_compute, 'Visible', 'off');
set(handles.preview_axis, 'Visible', 'off');
axes(handles.main_axis);


% --- Executes on button press in button_compute.
function button_compute_Callback(hObject, eventdata, handles)
% hObject    handle to button_compute (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

axes(handles.main_axis);
set(handles.button_3D, 'Enable', 'on');

scaling = sqrt((handles.xmax - handles.xmin)/(handles.txmax - handles.txmin));
if scaling > 0
    scaling = scaling /2;
end
handles.xmin = handles.txmin;
handles.xmax = handles.txmax;
handles.ymin = handles.tymin;
handles.ymax = handles.tymax;
if ~isfield(handles, 'grain')
    handles.grain = 1;
elseif isempty(handles.grain)
    handles.grain = 1;
end

switch handles.mode
    case -1 % logistic
        handles.space = compute_logistic(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.itern, handles.gridsize, 1);
    case 1 % mandelbrot
        handles.itern = handles.itern * scaling;
        handles.space = compute_mandelbrot_real(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.itern, handles.gridsize, 1);
    case 2 % julia
        handles.itern = handles.itern * scaling;
        handles.space = compute_julia(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.xjul, handles.yjul, handles.itern, handles.gridsize, 1);
    case 3 % newton
        handles.space = compute_newton(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.itern, handles.gridsize/handles.grain, 1);
    case 4 % user newton
        handles.space = compute_newton_power(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.itern, handles.gridsize/handles.grain, handles.ctes, 1);
    case 5 % barnsley
        handles.space = compute_barnsley(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.xjul, handles.yjul, handles.itern, handles.gridsize, 1);
    case 6 % circu poly
        if handles.arbitrary_mode == 1
            handles.space = compute_circumpoly(handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.xjul, handles.yjul, handles.itern, handles.gridsize/handles.grain, 1);
        else
            handles.space = compute_arbitrary(handles.equation, handles.xmin, handles.xmax, handles.ymin, handles.ymax, handles.xjul, handles.yjul, handles.itern, handles.gridsize/handles.grain, 1);
        end
    otherwise
        warning('CSE:Fractals:Render', 'Unknown Mode');
end
if isfield(handles, 'main_image')
    try delete(handles.main_image); end
end
handles = fillupdescription(handles);
if handles.mode > 0
    handles.main_image = image(handles.space, 'EraseMode', 'none');
    axis(handles.main_axis, 'off');
else % we have an [x y] in handles.space, not a complete table with handles.space(x, y) = color
    handles.main_image = plot(handles.space(:,1), handles.space(:,2), 'b.', 'MarkerSize', 1);
    axis(handles.main_axis, [handles.xmin handles.xmax handles.ymin handles.ymax]);
end

try delete(handles.preview_image); end
set(handles.txt_zoom_1, 'Visible', 'off');
set(handles.txt_zoom_2, 'Visible', 'off');
set(handles.button_cancel, 'Visible', 'off');
set(handles.button_compute, 'Visible', 'off');
set(handles.preview_axis, 'Visible', 'off');
% Update handles structure
guidata(hObject, handles);

% --------------------------------------------------------------------
function menu_head_program_Callback(hObject, eventdata, handles)
% hObject    handle to menu_head_program (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --------------------------------------------------------------------
function menu_help_Callback(hObject, eventdata, handles)
% hObject    handle to menu_help (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

%% UNTIL RELEASE, THIS FUNCTION IS USED FOR TESTING NEW ALGORITHMS %%

% return;
%% UNTIL RELEASE, THIS FUNCTION IS USED FOR TESTING NEW ALGORITHMS %%

helpmsg = sprintf(['CSE Fractals III\n\nA cross-platform matlab port from the Macintosh Software CSE Fractals II.\n\n' ...
        'Select in the menus the different types of fractals, according to which type of ' ...
        '"numbers" are used in the computation: Real, Imaginary, Quaternions, String Systems.\n\n' ...
        'More information of the different types of fractals is available on the internet. ' ...
        'Click on "More Info..." to go to a web-page with background infos avout chaos.']);
answr = questdlg(helpmsg, 'CSE Fractals III', 'More Info...', 'OK', 'OK');
if strcmp(answr, 'More Info...')
    % web('\\sust43\d$\cavin\Documents\web\fractals.html', '-browser');
    web('http://ltcmail.ethz.ch/cavin/fractals.html', '-browser');
end

% --------------------------------------------------------------------
function menu_quit_Callback(hObject, eventdata, handles)
% hObject    handle to menu_quit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

delete(handles.fractal_explorer);


% --------------------------------------------------------------------
function menu_mandelbrot_whole_Callback(hObject, eventdata, handles)
% hObject    handle to menu_mandelbrot_whole (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

handles.space = get_mandelbrot_initial(handles.gridsize);
handles.main_image = image(handles.space, 'EraseMode', 'none');
axis(handles.main_axis, 'off');

handles.xmin = -2;
handles.xmax = 1;
handles.ymin = -1.5;
handles.ymax = 1.5;
handles.itern = 70;
handles.mode = 1; % mandelbrot
handles = fillupdescription(handles);
set(handles.menu_julia_mouse, 'Enable', 'on'); % enables julia.
% Update handles structure
guidata(hObject, handles);

% --------------------------------------------------------------------
function menu_mandelbrot_user_Callback(hObject, eventdata, handles)
% hObject    handle to menu_mandelbrot_user (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

msg = sprintf('Mandelbrot Set:\n\nDefine Region and iterations:\n\n');
tmp = {num2str(handles.xmin), num2str(handles.xmax), num2str(handles.ymin), num2str(handles.ymax), num2str(handles.itern)};
tmp = localdlg({[msg 'Real Minimum:'], 'Real Maximum:', 'Imaginary Minimum:', 'Imaginary Maximum:', 'Iterations:'}, 'Mandelbrot Set', [1 10], tmp);
if isempty(tmp)
    return;