Merging fractal pictures with stunning animation and 3D effects

All the chaos came together

Well the screenshot speaks for itself.

%
% Example1: type mandel126 in the command line and the program will start. It doesn’t require any parameters and
% the GUI transfers all parameters automatically to its sub routines.
%
% Example2: in case you have trouble in getting mandel126 to work try the second version of the program which
% called mandel_klein in the command line. This program has a smaller GUI and should run on most computers.
%
% Example3: type GUIDE in the command line and then open mandel123.fig.
% You might have to use the browse function in the GUI window and navigate to the folder where you have downloaded the zipped mandel123 folder.
%
% Startup Picture
% The program always starts with the calculation of the Mandelbrot set with
% the coordinates R(-1.9 0.8) I(1.3 1.28) and it shows a 2D plot of the Mandelbrot set in low resolution.
%
%
%% Creating your own picture
% Press on the Zoom button within the View panel. The view will change to a 2D picture in case it was set to 3D.
% Note that the sliders in the Viewing Angle panel are now changed to 0 and 90 and the cursor has changed into a encircled +.
% Press the left mouse button on any position of the Mandelbrot set and then drag the mouse to another position to the left or right.
% You will note that with a slight delay a rectangle will be drawn around the select area and the program will zoom into the area.
% The next step is now to press the Re-calculate button which appeared after selecting the zoom mode and the program will execute a new calculation of the Mandelbrot Set.
% The picture will be automatically displayed.
%
%% Saving your picture
% Press the save button on right side of the graph and the picture
% coordinates and all settings saved. You can recall saved picture by
% selecting them in the popupmenu called saved Mandelbrot Sets.
%
%% Changing the Resolution
% This can be achieved by moving the slider in the Resolution panel on the right side of the GUI.
% Sliding to the right will increase the image resolution and which goes in hand with increased running time of the calculation.
% Please note that it is worth to increase the number of iterations as well to achieve the best results.
% It is sometimes best work on a moderate resolution (500- 700) and do all the zooming and change of
% viewing angle until happy with the result and then increase the resolution in the last step.
%
%% Mandelbrot Set Coordinates
% The current coordinates are always displayed in the textboxes on the right side of the GUI.
% Please note that after any zoom action all coordinates, viewing angle etc are also available in the command line interface.
% mandel =[0.1872426 0.5715756 0.2568356 0.6411687 700 500 112 15 3 29 70 3]
% These values correspond to the program handles: handles.lowerR
% handles.higherR
% handles.lowerI
% handles.higherI
% handles.stepsR
% handles.stepsI
% handles.MaxIter
% handles.col,
% handles.view
% handles.x_view
% handles.y_view
% handles.light
%
%% Number of Iterations
% This value determines how many times the calculation in the dummy2.m function is performed.
% Increasing this number might increase the running time of the program.
% It also can increase the image resolution. It is recommended to vary this parameter on
% the original Mandelbrot set and see which influence this parameter has.
% The effect is more pronounced when zooming deeper into the Mandelbrot Set.
%
%% Viewing Angle
% There are three elements in the viewing angle panel that will allow the user to manipulate the aspect ratio off the 3D Mandelbrot set.
% 3D Rotate button: clicking on this button changes the appearance off the mouse curser.
% Left click and move the mouse and the aspect ratio of the 3D image is going to change and the mouse
% enables you view the Mandelbrot set from any angle just by moving the mouse.
%
% The 2 sliders in the Viewing angle panel enable you to change the viewing angle of the Mandelbrot set.
% In order to experiment with these sliders it is recommended to reduce the Resolution of the picture
% and recalculate the current image by pressing the Re-calculate button.
% As a result changes in the aspect ratio happen in real time (depending on your computer of course).
%
%
%% Chose colour
% This program comes with the standard set of Matlab colourmaps as well as four custom colormaps.
% Please select them from the Chose colour popupmenu.
%
%% Load Colourmap editor
% It is possible to load the standard Matlab colour editor and change the current colormap.
% Once you have changed the
%
%% Save CMAP
% Press the CMAP button and the current colormap is saved. You can recall
% this colormap in the Chose Colour popup menu. The program automatically
% asigns a name to the colormap.
%
%% Saved Mandelbrot Sets
%
% This version of the mandel12x