LOGO-L> Recursive curve mania

[George Mills <mills@softronix.com>]

to aaa
;
; You can generate any number of curves (Koch, Hilbert, Peano etc.)
; with this. By just defining a new expression. This is the
; same approach used in the 3D HilbertCube I posted.
; 
; See the web page below for the different equations.
;
; Note: I used P for + and M for - in the equations.
;
; Note: In the Koch example F is both a graphics function
; (forward) and it's a recursive function. To deal with this
; I replaced all "F" with "FX" and let X do the recursion
; and F do the graphics.
;
; Note: All that I have done here is implement something
; close to the "Strings" method which is just a shorthand
; way to describe the curve. That is, the ultimate one-liner.
;
; http://forum.swarthmore.edu/advanced/robertd/lsys2d.html
;
; Note: You could take this a step further by actually
; "parsing" the same String Equations, recursively expand the
; strings and define the functions on the fly.
;
cs pr [Sierpinski arrowhead]
DoFunction [Y F] [Y F P X F P Y] [X F M Y F M X] 60 5 6
wait 120

cs pr [Square]
DoFunction [F P X F P F P X F] [X F M F P F M X F P F P X F M F P F M X]
[] 90 5 4
wait 120

cs pr [Koch]
DoFunction [X] [X F P X F M M X F P X F] [] 60 5 4
wait 120

cs pr [Hilbert curve]
DoFunction [X] [P Y F M X F X M F Y P] [M X F P Y F Y P F X M] 90 5 5
wait 120

cs pr [Dragon]
DoFunction [X] [X P Y F P] [M F X M Y] 90 5 12
wait 120

pu
home
pd
pr [Done]
end

to DoFunction :function_root :function_of_x :function_of_y :angle :siz
:lev
; We are at the top level and we don't want X or Y to decrement :lev
make "lev :lev + 1
; Run the base equation (all arguments are passed down implicity)
run :function_root
end

to F
; :siz and :lev implicity passed from FX or FY or DoFunction
setpc :lev
sound (list 200*:lev (:lev*20))
fd :siz
end

to FX :siz :lev
; :function_of_x implicity passed from DoFunction
if :lev > 0 [run :function_of_x]
end

to FY :siz :lev
; :function_of_y implicity passed from DoFunction
if :lev > 0 [run :function_of_y]
end

to M
; :angle implicity passed from DoFunction
lt :angle
end

to P
; :angle implicity passed from DoFunction
rt :angle
end

to X
; :siz and :lev implicity passed from FX or FY or DoFunction
fx :siz :lev-1
end

to Y
; :siz and :lev implicity passed from FX or FY or DoFunction
fy :siz :lev-1
end

-- 
===============================================================
George Mills (mills@softronix.com)
http://www.softronix.com/
The www page contains some very powerful educational software.
Our single most important investment is our kids.
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