Geometry exploration

This collection of shapes is the result of my learning the LOGO programming language.  

Sierpinski triangles interpretation

I wanted to create recursive or fractal patterns similar to the ferns already created, or other natural elements using mathematical formulae, eg. sunflowers using the Fibonacci sequence.  So first I tried creating the Sierpinksi triangles - triangles within triangles, each one a quarter the size of the next largest.  

PD
REPEAT 3 [FD 10 LT 120]
FD 5
LT 60
REPEAT 3 [FD 5 LT 120]
FD 2.5
LT 60
REPEAT 3 [FD 2.5 LT 120]
FD 1.25
LT 60
REPEAT 3 [FD 1.25 LT 120]
FD .625
LT 60
REPEAT 3 [FD .625 LT 120]
FD .3125
LT 60
REPEAT 3 [FD .325 LT 120]
PU
WEST 20

This didn't really use any of LOGO's recursive ability, so I tried understanding how to make the code more condensed.

Defining new objects & metapatterns

The circle-like shape made of 36 repeated squares shows my understanding of how to define new objects in LOGO to use as shortcuts when creating an object which recurs.  

PD
TO square
REPEAT 4 [FD 10 LT 90]
END
REPEAT 36[square RT 10]
PU
SOUTH 20

TO tree :size
IF :size < 2 [STOP]
FD :size
LT 30
tree :size * (7/10)
RT 60
tree :size * (7/10)
LT 30
tree :size * (7/10)
RU 30
tree :size * (7/10)
RD 60
tree :size * (7/10)
RU 30
BK :size
END
RU 90
PD
tree 10
PU