Flower Bed

Recently I investigated Apollonian gaskets (a type of space-filling fractal composed of ever-repeating circles) for use as 'pore-space fillers' in a model I am creating for synthetic sediment beds. I came across a most excellent script here:

http://www.mathworks.com/matlabcentral/fileexchange/15987

In my Friday afternoon boredom, I have just modified some aspects of the program to create a function which simulates a pretty flower bed

	function flower_bed(n)
	% n is the number of internal circles (must be greater than 2 - greater than 10 looks weird)
	h = figure;
	hAxs = axes('Parent',h);
	axis equal;
	grid off;
	hold on;
	V = 0:2*pi/n:2*pi;
	V = V +pi/2;
	cV = cos(V);
	sV = sin(V);
	d = sqrt(diff(cV).^2+diff(sin(V)).^2);
	r = d(1)/2;
	ratio = max(max(max(abs(cV+r)),max(abs(sV+r))),...
	max(max(abs(cV-r)),max(abs(sV-r))));
	cV = cV/ratio;
	sV = sV/ratio;
	r = r/ratio;
	r_inner1 = sqrt(cV(1).^2+sV(1).^2) - r;
	for k=1:2:11
	for j=1:2:11
	S(1).x = [k,k,k+cV(1:end-1)];
	S(1).y = [j,j,j+sV(1:end-1)];
	S(1).r = [1,r_inner1,r*ones(1,n)];
	hAxs = plot_circles(hAxs,S,1);
	end
	end
	axis off
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	function hAxs = plot_circles(hAxs,S,n,display_style)
	hold on
	for t=1:size(S(n).x,2)
	rectangle('Position',[S(n).x(t)-S(n).r(t),...
	S(n).y(t)-S(n).r(t),2*S(n).r(t),2*S(n).r(t)],...
	'Curvature',[1,1],'LineWidth',0.5,...
	'tag',num2str(n),'Parent',hAxs,'EdgeColor','k','FaceColor',[rand rand rand]);
	% plot(S(n).x(t),S(n).y(t),'k+','tag',num2str(n));
	end

view raw flowerbed.m hosted with ❤ by GitHub

Some example outputs below - enjoy! Right, now back to work ...