LOGO-L> Understanding Recursion

[Yehuda Katz <yehuka@beitberl.ac.il>]

Hello Turtlers,

One of the most difficult topics in CS is the idea of recursion.
Teachers spend a considerable amount of effort to make it clear for
students. Harvey devoted in his CSLS many pages and different approaches
and
metaphors for explaining recursion.

In addition, I use the following tiny program, to visualize on the
screen how recursion works. The key is the use of colors. Each color
reptesents its level of depth: blue denotes depth 1, green denotes level
2 etc., according to the single-index colors used in UCBLogo.

To run the program in MSWLogo say, e.g., DRAW 60 5; the first number is
the size, the second number is the maximal depth.

========================
to draw :size :level
if :level<1[stop]
repeat 3[pattern rt 120]
end

to pattern
setucbpc :level    ; (1)
bk :size
fd :size
pu fd :size pd     ; (2)
draw :size/2 :level-1
pu bk :size pd
end
========================

Remarks:

(1)     For UCBLogo replace SETUCBPC by SETPC.

(2)     To visualize step-by-step how the image is built up, replace
this
remark by ERN RC. Now, after each stage, Logo stops and waits for the
next key press. Watch carefully to see what goes "behind the curtains".
You can also TRACE the program.

Enjoy it,

[[Yehuda]]