%%% Pythagorean tree

\def\dir{2011/kees-van-der-laan/}
\immediate\pdfximage width.8\hsize{\dir/pyta.pdf}
\centerline{\pdfrefximage\pdflastximage}

\beginverbatim
/sq{ 0 0 moveto s 0 rlineto 0 s rlineto s neg 0 rlineto
	closepath stroke } def
/pythagoreantree { sq                           % draw the square
	1 sub dup 0 ge
	{ gsave
		0 s translate 45 rotate .7071 dup scale % transform user space
		pythagoreantree                         % do it again, Sam
		grestore
		.5 s mul 1.5 s mul translate
		-45 rotate .7071 dup scale              % transform user space
		pythagoreantree                         % do it again, Sam
	} if 1 add
} def
/s 50 def
11 pythagoreantree pop
showpage
\endverbatim

Bosboom drew the tree in the 1940-ies by hand, Lauwerier (1986): {\it Fractals,
meetkundige figuren in eindeloze herhaling\/}, Aramith, programmed them
nonrecursively in Basic, and me, captivated by the path datastructure and its
operators, in \METAFONT\ in the mid-90-ies. Undoubtedly many others have drawn
the tree since the PC entered our homes. It was an illustration in the 1972 CWI
calendar, from which I borrowed the $\pi$-decimals 2010 pearl.

However, PostScript, which is with us for 30 years already, mind you, allows to
transform, rotate and scale user space. A very powerful facility, and together
with recursion extremely useful for drawing these kind of fractals, where it is
all about one element, redrawn translated, scaled or rotated.

The {\it Thinking in PostScript\/} (1990) book (for free on the WWW) states that it is
silly to program fractals in PS. No longer true since we can transform PS into
PDF, canned for inclusion in \TeX\ documents.

More about Pythagoras Trees soon in MAPS!