function GoldenSpiralLogarithmic() % source code for drawings the animations % % 2018-06-07 Jahobr  fps = 50; nFrames = 245; xySize = 450; % gif size in pixel  scaleReduction = 2; % the size reduction: adds antialiasing  [pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location  figHandle = figure(2324455); clf axesHandle = axes; hold(axesHandle,'on') set(figHandle, 'Units','pixel'); set(figHandle, 'position',[1 1 xySize*scaleReduction xySize*scaleReduction]); % big start image for antialiasing later [x y width height] set(figHandle, 'GraphicsSmoothing','on') % requires at least version 2014b set(axesHandle,'position',[-0.05 -0.05 1.1 1.1]); % stretch axis bigger as figure, easy way to get rid of ticks [x y width height] axis equal; drawnow;  phi = (1+sqrt(5))/2; b = log(phi)/(pi/2);  thetaXextreme = atan(b)+pi/2*(2:-2:-20); rXextreme = phi.^(thetaXextreme*2/pi); [Xextreme,yXext] = pol2cart(thetaXextreme,rXextreme);  thetaYextreme = atan(b)+pi/2*(1:-2:-21); rYextreme = phi.^(thetaYextreme*2/pi); [xYext,Yextreme] = pol2cart(thetaYextreme,rYextreme);  theta = pi/2*(3:-0.02:-20); % curve points r = phi.^(theta*2/pi); % radii [X,Y] = pol2cart(theta,r); % cartesian coordinate system  for useColor = [false true]     cla(axesHandle);          for m = 1:numel(Xextreme)-2                  if useColor             cmap = [0.0 0.0 0.0;... 1 spiral color; black                     0.3 0.3 0.3;... 2 box-edge color; grey                     1.0 0.8 0.8;... 3 box-filling; pale red                     1.0 1.0 0.7;... 4 box-filling; pale yellow                     0.8 1.0 0.8;... 5 box-filling; pale green                     0.8 0.8 1.0]; % 6 box-filling; pale blue             cmap = round(cmap.*255)./255; % round to uint8 positions             curVers = '_color';             if Xextreme(m)<0                 colFilling = cmap(3,:); % pale red             else                 colFilling = cmap(4,:); % pale yellow             end             patch([Xextreme(m)   Xextreme(m) Xextreme(m+2) Xextreme(m+2) Xextreme(m)],...                 [  Yextreme(m+1) Yextreme(m) Yextreme(m)   Yextreme(m+1) Yextreme(m+1)],...                 colFilling,'EdgeColor',cmap(2,:),'LineWidth',3)                          if Yextreme(m)<0                 colFilling = cmap(5,:); % pale green             else                 colFilling = cmap(6,:); % pale blue             end             patch([Xextreme(m+2) Xextreme(m+2) Xextreme(m+1) Xextreme(m+1) Xextreme(m+2)],...                 [  Yextreme(m+2) Yextreme(m)   Yextreme(m)   Yextreme(m+2) Yextreme(m+2)],...                 colFilling,'EdgeColor',cmap(2,:),'LineWidth',3)                      else             cmap = [0.0 0.0 1.0;... 1 spiral color; blue                     0.0 0.0 0.0;... 2 box-edge color; black                     1.0 1.0 1.0]; % 3 box-filling; white             cmap = round(cmap.*255)./255; % round to uint8 positions             curVers = '';             plot([Xextreme(m)   Xextreme(m) Xextreme(m+2) Xextreme(m+2) Xextreme(m)],...                 [ Yextreme(m+1) Yextreme(m) Yextreme(m)   Yextreme(m+1) Yextreme(m+1)],...                 '-','color',cmap(2,:),'LineWidth',3)             plot([Xextreme(m+2) Xextreme(m+2) Xextreme(m+1) Xextreme(m+1) Xextreme(m+2)],...                 [ Yextreme(m+2) Yextreme(m)   Yextreme(m)   Yextreme(m+2) Yextreme(m+2)],...                 '-','color',cmap(2,:),'LineWidth',3)          end     end          plot(X,Y,'.-','linewidth',5,'color',cmap(1,:),'Markersize',5*3.4) % plot spiral      scale = linspace(log(-Xextreme(3)),log(-Xextreme(5)),nFrames+1); % start with an area fully covered, zoom in till repetition     scale = exp(scale); % logarithmic sale     scale = scale(1:end-1); % cut off doubled frame          RGBimageStack = uint8(ones(xySize*scaleReduction,xySize*scaleReduction,3,nFrames)); % allocate     for iFrame = 1:nFrames                  axis equal         xlim([-scale(iFrame) scale(iFrame)]) % zoom         ylim([-scale(iFrame) scale(iFrame)]) % zoom         drawnow expose; % causes graphics and user-interface objects to refresh with all pending changes          % save SVG         if iFrame == 1 % only once             if ~isempty(which('plot2svg'))                 posSave = get(figHandle, 'position');                 set(figHandle, 'position',[1 1 800 800]); % big start image for antialiasing later [x y width height]                 plot2svg(fullfile(pathstr, [fname curVers '.svg']),figHandle) % by Juerg Schwizer                 set(figHandle, 'position',posSave); % reset size                 set(axesHandle,'position',[-0.05 -0.05 1.1 1.1]); % stretch axis bigger as figure, easy way to get rid of ticks [x y width height]             else                 disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');             end         end                  %% save animation         f = getframe(figHandle);         RGBimageStack(:,:,:,iFrame) = f.cdata; % store      end          reducedRGBimage = imReduceSize(RGBimageStack,scaleReduction); % the size reduction: adds better antialiasing     map = createImMap(reducedRGBimage,32,cmap); % colormap      im = uint8(ones(xySize,xySize,1,nFrames)); % allocate colormap indexed image     for iFrame = 1:nFrames         im(:,:,1,iFrame) = rgb2ind(reducedRGBimage(:,:,:,iFrame),map,'nodither'); % RGB  to  colormap indexed image     end      imwrite(im,map,fullfile(pathstr, [fname curVers '_in.gif']),'DelayTime',1/fps,'LoopCount',inf) % save gif     disp([fname curVers '_in.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit     imwrite(im(:,:,:,iFrame:-1:1),map,fullfile(pathstr, [fname curVers '_out.gif']),'DelayTime',1/fps,'LoopCount',inf) % save gif      %% save MP4 and WebM     cd(pathstr); % set path to working folder     videoFileName = [fname curVers '_in'];      vid = VideoWriter(videoFileName,'MPEG-4'); % Prepare the new file     vid.FrameRate = fps;     vid.Quality = 100; % quality in [0% 100%]     open(vid);     for iRep = 1:5 % loops         for iFrame = 1:nFrames             writeVideo(vid,RGBimageStack(:,:,:,iFrame));         end     end     close(vid); %     disp('conversion from MP4 to WebM (Matlab currently does not support webm)');     try         dosCommand = ['!ffmpeg -i ' videoFileName '.mp4 '...   % Command and source             '-c:v libvpx-vp9 -crf 30 -b:v 0 -deadline best '...% constant (best) quality; see: https://trac.ffmpeg.org/wiki/Encode/VP9             videoFileName '.webm'];                            % conversion target         eval(dosCommand); % run conversion from mp4 to webm     catch         disp(['"ffmpeg.exe" not available in path "' pathstr '" (or other problem); see https://ffmpeg.zeranoe.com/builds/']);     end end   function im = imReduceSize(im,redSize) % Input: %  im:      image, [imRows x imColumns x nChannel x nStack] (unit8) %                      imRows, imColumns: must be divisible by redSize %                      nChannel: usually 3 (RGB) or 1 (grey) %                      nStack:   number of stacked images %                                usually 1; >1 for animations %  redSize: 2 = half the size (quarter of pixels) %           3 = third the size (ninth of pixels) %           ... and so on % Output: %  imNew:  unit8([imRows/redSize x imColumns/redSize x nChannel x nStack]) % % an alternative is : imNew = imresize(im,1/reduceImage,'bilinear'); %        BUT 'bicubic' & 'bilinear'  produces fuzzy lines %        IMHO this function produces nicer results as "imresize"   [nRow,nCol,nChannel,nStack] = size(im);  if redSize==1;  return;  end % nothing to do if redSize~=round(abs(redSize));             error('"redSize" must be a positive integer');  end if rem(nRow,redSize)~=0;     error('number of pixel-rows must be a multiple of "redSize"');  end if rem(nCol,redSize)~=0;  error('number of pixel-columns must be a multiple of "redSize"');  end  nRowNew = nRow/redSize; nColNew = nCol/redSize;  im = double(im).^2; % brightness rescaling from "linear to the human eye" to the "physics domain"; see youtube: /watch?v=LKnqECcg6Gw im = reshape(im, nRow, redSize, nColNew*nChannel*nStack); % packets of width redSize, as columns next to each other im = sum(im,2); % sum in all rows. Size of result: [nRow, 1, nColNew*nChannel] im = permute(im, [3,1,2,4]); % move singleton-dimension-2 to dimension-3; transpose image. Size of result: [nColNew*nChannel, nRow, 1] im = reshape(im, nColNew*nChannel*nStack, redSize, nRowNew); % packets of width redSize, as columns next to each other im = sum(im,2); % sum in all rows. Size of result: [nColNew*nChannel, 1, nRowNew] im = permute(im, [3,1,2,4]); % move singleton-dimension-2 to dimension-3; transpose image back. Size of result: [nRowNew, nColNew*nChannel, 1] im = reshape(im, nRowNew, nColNew, nChannel, nStack); % putting all channels (rgb) back behind each other in the third dimension im = uint8(sqrt(im./redSize^2)); % mean; re-normalize brightness: "scale linear to the human eye"; back in uint8   function map = createImMap(imRGB,nCol,startMap) % createImMap creates a color-map including predefined colors. % "rgb2ind" creates a map but there is no option to predefine some colors, %         and it does not handle stacked images. % Input: %   imRGB:     image, [imRows x imColumns x 3(RGB) x nStack] (unit8) %   nCol:      total number of colors the map should have, [integer] %   startMap:  predefined colors; colormap format, [p x 3] (double)  imRGB = permute(imRGB,[1 2 4 3]); % step1; make unified column-image (handling possible nStack) imRGBcolumn = reshape(imRGB,[],1,3,1); % step2; make unified column-image  fullMap = double(permute(imRGBcolumn,[1 3 2]))./255; % "column image" to color map  [fullMap,~,imMapColumn] = unique(fullMap,'rows'); % find all unique colores; create indexed colormap-image % "cmunique" could be used but is buggy and inconvenient because the output changes between "uint8" and "double"  nColFul = size(fullMap,1); nColStart = size(startMap,1); disp(['Number of colors: ' num2str(nColFul) ' (including ' num2str(nColStart) ' self defined)']);  if nCol<=nColStart;  error('Not enough colors');        end if nCol>nColFul;   warning('More colors than needed');  end  isPreDefCol = false(size(imMapColumn)); % init   for iCol = 1:nColStart     diff = sum(abs(fullMap-repmat(startMap(iCol,:),nColFul,1)),2); % difference between a predefined and all colores     [mDiff,index] = min(diff); % find matching (or most similar) color     if mDiff>0.05 % color handling is not precise         warning(['Predefined color ' num2str(iCol) ' does not appear in image'])         continue     end     isThisPreDefCol = imMapColumn==index; % find all pixel with predefined color     disp([num2str(sum(isThisPreDefCol(:))) ' pixel have predefined color ' num2str(iCol)]);     isPreDefCol = or(isPreDefCol,isThisPreDefCol); % combine with overall list end [~,mapAdditional] = rgb2ind(imRGBcolumn(~isPreDefCol,:,:),nCol-nColStart,'nodither'); % create map of remaining colors map = [startMap;mapAdditional];