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File:Spiral of black and white squares 10 till repetition spiraling in.gif

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Original file (1,000 × 1,000 pixels, file size: 1.79 MB, MIME type: image/gif, looped, 50 frames, 1.0 s)

Summary

Description
Deutsch: Sich wiederholende, schwarze und weiße Quadrate.
English: Self-similar, repeating black and white squares.
Date
Source Own work
Author Jahobr
Other versions
GIF development
InfoField
 
This diagram was created with MATLAB by Jahobr.
Source code
InfoField

MATLAB code

function Spiral_of_black_and_white_squares()
% source code for drawing the animation
%
% 2017-04-26 Jahobr

fps = 50;
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location

figHandle = figure(15124455);
clf
axesHandle = axes;
hold(axesHandle,'on')
set(figHandle, 'Units','pixel');
set(figHandle, 'position',[1 1 1000 1000]); % set default
set(axesHandle,'position',[0 0 1 1]); % stetch axis bigger as figure, easy way to get rid of ticks [x y width hight]
set(figHandle,'GraphicsSmoothing','on') % requires at least version 2014b

L(1) = 1; % definition, length of first square

xyLim = [-L(1) L(1)]*0.99;
xlim(xyLim); ylim(xyLim); % set axis limits
axis equal; drawnow;

for nSquaresTillRep = [4 10] % ONLY EVEN NUMBERS! number of squares till the orientation repeats (90°)
    
    alpha = pi/2/nSquaresTillRep;
    
    %    +--a1--+==----b1------+
    %    I     /   ----____    a1
    %    b1   /            ----+
    %    I   /            90° /I<-alpha
    %    I  /                / I
    %    I /                /  I
    %    I/                /   b1
    %    +---___          /    I
    %    a1     ----___  /     I
    %    +----b1-------=+--a1--+
    
    for index = 1:nSquaresTillRep+1
        % L = a+b
        % tan(alpha) = a/b; tan(alpha)*b = a
        % 1 = tan(alpha)*b+b = b*(tan(alpha)+1)
        b(index) = L(index)/(tan(alpha)+1);
        a(index) = L(index)-b(index);
        
        L(index+1) = sqrt(a(index)^2+b(index)^2); % side length of inner square
    end
    
    for currentCase = 1:2
        switch currentCase
            case 1 % zoom
                nFrames = 200;
                set(figHandle, 'position',[1 1 500 500]); % 
                method = 'zooming_in';
                endVal = log( 1/L(nSquaresTillRep+1) );
                scale = linspace(0,endVal,nFrames+1);
                
                scale = exp(scale);
                scale = scale(1:end-1); % cut of doubled frame
                rotImage = linspace(0,-pi/2,nFrames+1);
                rotImage = rotImage(1:end-1); % cut of doubled frame
            case 2 % spiral
                if nSquaresTillRep == 4
                    nFrames = 100;
                    set(figHandle, 'position',[1 1 700 700]); % 
                elseif  nSquaresTillRep == 10
                    nFrames = 50;
                    set(figHandle, 'position',[1 1 1000 1000]); % 
                else
                    error('not defined')
                end
                method = 'spiraling_in';
                endVal = log( 1/L(3) );
                scale = linspace(0,endVal,nFrames+1);
                
                scale = exp(scale);
                scale = scale(1:end-1); % cut of doubled frame
                rotImage = linspace(0,-2*alpha,nFrames+1);
                rotImage = rotImage(1:end-1); % cut of doubled frame
        end
        
        sb = b(1); % scale square down one itteration (assuming  a(1)+b(1)=1)
        sa = a(1); % scale square down one itteration (assuming  a(1)+b(1)=1)
        
        for iFrame = 1:nFrames
            cla(axesHandle) % fresh frame
            
            col = [0 0 0]; % start black
            
            curScale = scale(iFrame);
            x = curScale*[-L(1) -L(1) L(1)  L(1)]; % make base square bigger, to "zoom in"
            y = curScale*[-L(1)  L(1) L(1) -L(1)]; % make base square bigger, to "zoom in"
            
            if currentCase == 2 % rotate base square
                rotM = [cos(-rotImage(iFrame)) -sin(-rotImage(iFrame)); sin(-rotImage(iFrame)) cos(-rotImage(iFrame))];
                vecTemp = rotM*[x; y];
                x = vecTemp(1,:);
                y = vecTemp(2,:);
            end
            
            while norm([x(1) y(1)]) > 0.5/900 % squares smaller than a pixel
                
                patch([x x(1)],[y y(1)],col,'EdgeColor','none');
                
                col = 1-col; % flip color
                
                x = [sb*x(1)+sa*x(2)  sb*x(2)+sa*x(3)  sb*x(3)+sa*x(4)  sb*x(4)+sa*x(1)]; % create next square
                y = [sb*y(1)+sa*y(2)  sb*y(2)+sa*y(3)  sb*y(3)+sa*y(4)  sb*y(4)+sa*y(1)]; % create next square
                
            end
            
            %% save animation
            xlim(xyLim); ylim(xyLim); % set axis limits
            drawnow % update figure window and execute pending callbacks
            pause(0.01)
            
            f = getframe(figHandle);

            if iFrame== 1
                map = gray(8); % 8 colors % create color map % or use : [im,map] = rgb2ind(f.cdata,4,'nodither'); % 
                im = rgb2ind(f.cdata,map,'nodither'); % create first image
                
                im(1,1,1,nFrames) = 0; % allocate
                if currentCase == 1
                    if ~isempty(which('plot2svg'))
                        plot2svg(fullfile(pathstr, [fname '_' num2str(nSquaresTillRep)  '_till_repetition.svg']),figHandle) % by Juerg Schwizer, See http://www.zhinst.com/blogs/schwizer/
                    else
                        disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
                    end
                end
            end
            
            imtemp = rgb2ind(f.cdata,map,'nodither');
            im(:,:,1,iFrame) = imtemp;
            
        end
        imwrite(im,map,fullfile(pathstr, [fname '_'  num2str(nSquaresTillRep) '_till_repetition_' method '.gif']),'DelayTime',1/fps,'LoopCount',inf) % save gif
        disp([fname '_'  num2str(nSquaresTillRep) '_till_repetition_' method '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
    end
end

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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Date/TimeThumbnailDimensionsUserComment
current22:36, 12 September 2017Thumbnail for version as of 22:36, 12 September 20171,000 × 1,000 (1.79 MB)JahobrGraphicsSmoothing with matlab version 2017a, 8 colores, more pixel
09:06, 26 April 2017Thumbnail for version as of 09:06, 26 April 2017450 × 450 (562 KB)JahobrUser created page with UploadWizard

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