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Great Hall Floor and Maple

vv 13143 Maple
September 01 2018
13

I have recently visited the Queen's House at Greenwich  (see wiki),  an  important building in British architectural history (17th century).
I was impressed by the Great Hall Floor, whose central geometric decoration seems to be generated by a Maple program :-)

Here is my code for this. I hope you will like it.

restart;
with(plots): with(plottools):
n:=32: m:=3:#    n:=64: m:=7:

a[0], b[0] := exp(-Pi*I/n), exp(Pi*I/n):
c[0]:=b[0]+(a[0]-b[0])/sqrt(2)*exp(I*Pi/4):  
for k to m+1 do  
  c[k]:=a[k-1]+b[k-1]-c[k-1];
  b[k]:=c[k]*(1+exp(2*Pi*I/n))-b[k-1];
  a[k]:=conjugate(b[k])  od:
b[-1]:=c[0]*(1+exp(2*Pi*I/n))-b[0]:
a[-1]:=conjugate(b[-1]):
c[-1]:=a[-1]+b[-1]-c[0]:
seq( map[inplace](evalf@[Re,Im], w), w=[a,b,c] ):
Q:=polygonplot([seq([a[k],c[k],b[k],c[k+1]],k=0..m-1), [c[m],a[m],b[m]], [a[-1],b[-1],c[0]]]):
display(seq(rotate(Q, 2*k*Pi/n, [0,0]),k=0..n-1), disk([0,0],c[m][1]/3), axes=none, size=[800,800], color=black);

rotate

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