First Forward into Logo 11: Sequences

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
Age
11 to 18
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

First Forward Into Logo

Previous: FF10

 

Consider the following procedure which uses two variables:
(Warning - you may have to press HALT to stop this procedure.)
TO LOP :X :Y
PR :X
WAIT 120
LOP :Y :X + :Y
END


What do you think is happening this time?
Try 'chasing' through the procedure the values: x = 1 and y = 1.
No longer surprised!
Why do you think it goes on and on...?
Yes it keeps starting itself again, but with different variables,
moving on in the sequence by adding the last two variables.


Why not experiment further changing the fourth line?
For example:
LOP :Y :X +:Y*2
LOP :Y :X - :Y*2
LOP :Y :X * 2


Any surprises?


LOP :Y * 2 :X + :Y


Etc. Etc. Etc....


 
1
1
3
5
11
21
43
85
171
341
683
1365
2731
5461
10923
21845
43691
87381
174763
349525
699051
1398101
2796203
5592405
11184811
22369621
44739243
89478485
178956971
357913941

 

Next: FF12