e = 'ENCINAL ULTIMATE';
w = 'www.vangregory.com/ultimate/';
cN = exp((1:400)*pi*2j/399);   % 400 point unit circle

% Parametric curve disc design ------------------------------------------

a = .485;  b = 6.5;
t0 = pi*(.34: .027 : 1.23);  r0 = .6 ./ (t0.^.8);  p0 = r0.*exp(t0.*1j); % text spiral
t1 = pi*(a  : .001 : b   );  r1 =  1 ./  t1;       p1 = r1.*exp(t1.*1j); % red spiral
t2 = pi*(a+2: .001 : b+3 );  r2 = 40 ./ (t2.^2);   p2 = r2.*exp(t2.*1j); % blue spiral
cntr = complex(-.1,.15);  circ = .55*cN;
plt(circ+cntr,p1,p2,'position',[10 45 1309 1087],'linewidth',4,...
    'TraceC',[.9 .9 .9; 1 0 0; 0 0 1],'xlim',[-.8 .56],'ylim',[-.45 .75]);

text(.0382,-.1735,'r = 1/\theta','color',[1 0 0],'fontsize',20,'rotation',38);
text(.1028,-.264,'r = 40/\theta^2','color',[0 0 1],'fontsize',20,'rotation',43);

for k=1:length(e)
  m=2*k;  v = p0(m+1) - p0(m-1);
  text(real(p0(m)),imag(p0(m)),e(k),'color',[.7 0 .7],...
      'rotation',angle(v)*180/pi,'fontsize',800*abs(v),...
      'fontname','Lucida Handwriting');
end;
for k=1:length(w)
  p = .93*circ(130+3*k) + cntr;
  text(real(p),imag(p),w(k),'color',[.5 .5 .5],'fontsize',24,...
  'rotation',90+angle(p-cntr)*180/pi,'fontname','Andale Mono');
end;

% 12 circles disc design ------------------------------------------
% note: This design is one solution to the problem below:
%
%      *****************************************************
%      **                                                 **
%      **            The 12 circle problem:               **
%      **    Draw 12 circles in a plane so that every     **
%      **    circle is tangent to exactly 5 others.       **
%      **                                                 **
%      *****************************************************
%
v = 1:4;  r = (12+5*v)./(12-v); % radii of vertical set of 4
c = [v-1 complex(4,7-r) 9-v];   % center location of all 12 circles
r = [v r v];                    % radii of all 12 circles
tc = [.75 .75 0; 1 0 0; .7 0 .7; 0 0 1];  % colors for each group of 4 circles
cntr = complex(4,1.5);  circ = 6.5*cN;
plt(circ+cntr, transpose(cN)*r + repmat(c,400,1),...
    'TraceC',[.9 .9 .9; tc; tc; tc],...
    'LineWidth',4,'Position',[15 15 1188 1115],...
    'Xlim',[-3.5  11.5],'Ylim',[-6 9],...
    'AxisPos',[1 1 1 1 1.2],'LabelY','','LabelX','');
set(findobj('marker','+'),'vis','off');
for k=1:length(e)
  p = .93*circ(mod(6*k-29,400)) + cntr;
  text(real(p),imag(p),e(k),'color',[0 0 0],'fontsize',34,...
      'rotation',90+angle(p-cntr)*180/pi,'fontname','Lucida Handwriting');
end;
for k=1:length(w)
  p = .93*circ(130+3*k) + cntr;
  text(real(p),imag(p),w(k),'color',[.5 .5 .5],'fontsize',24,...
       'rotation',90+angle(p-cntr)*180/pi,'fontname','Andale Mono');
end;