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Nature, Spirals, Math, & Art
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Nature, Spirals, Math, & Art
peter@codetolearn.ca
Go to lynxcoding.club and get a free account if you’re Canadian!
Go to ALL Projects.
Open the Math Folder
Click on Public: Nature, Spirals, Math and Art
NOTE:
These are DRAFT!
Nature, Spirals, Math, & Art
Navigate to the "Simple Spirals" Page
AND
To the "Simple Spirals" Procedure Pane
(if you are not already there!)
Nature, Spirals, Math, & Art
Single Variable (square :size)
to square :size
repeat 4 [fd :size rt 90]
end
Let’s change the pensize to 3
Setpensize 3
Simple Spirals
to spiral :step :angle
fd :step
rt :angle
spiral :step + 5 :angle
end
try:
spiral 0 50
WOWEE! What happened?!
It doesn’t stop!!! And it’s too fast!!
Slow it Down
Let’s see it happening better
Put in a wait command
Add in wait 3
fd :step
rt :angle
wait 3
spiral :step + 5 :angle
end
Aha! Keeps going! Why?
Nature, Spirals, Math, & Art
Add a Condition!
Add in:
if :step = 100 [stop]
to spiral :step :angle
if :step = 100 [stop]
fd :step
rt :angle
wait 3
spiral :step + 5 :angle
end
Watch This!
Now type
spiral 1 50
What happened!?
WHY?
We have to change it from = to >:
to spiral :step :angle
if :step > 100 [stop]
fd :step
rt :angle
wait 3
spiral :step + 5 :angle
end
Nature, Spirals, Math, & Art
MAKE CHANGES
Now what is available to change?
Step, angle at the execution!
Step, angle in the procedure!
EXECUTION
CHANGE THE STEP
Now, let’s just change the fd and see the differences
spiral 10 50
cg
spiral 20 50
cg
spiral 30 50
It’s hard to see the difference
So let’s send the turtle HOME each time
cg
spiral 1 50
pu
home
pd
spiral 10 50
pu
home
pd
spiral 30 50
hmmmm still hard to see the difference
let’s change the colours each time
spiral 1 50
pu
home
pd
setc 'red
spiral 10 50
pu
home
pd
setc 'blue
spiral 30 50
So we can see that it is that FIRST step that is the biggest. After that, things look fairly similar. Why?
Nature, Spirals, Math, & Art
CHANGE THE ANGLE
Spiral 1 50
pu
home
pd
setc 'red
spiral 1 80
pu
home
pd
setc 'blue
spiral 1 120
Nature, Spirals, Math, & Art
PROCEDURE
NOW CHANGE THE PROCEDURE
CHANGE THE STEP
Type spiral 1 30
Ok
Change the STEP to 1
to spiral :step :angle
if :step > 100 [stop]
fd :step
rt :angle
wait 3
spiral :step + 1 :angle
end
Type spiral 1 30
Change the STEP to .5
to spiral :step :angle
if :step > 100 [stop]
fd :step
rt :angle
wait 3
spiral :step + .5 :angle
end
Change the STEP to .2
What if we use NEGATIVE numbers?
e.g., :step - 5
Nature, Spirals, Math, & Art
CHANGE THE ANGLE
to spiral :step :angle
if :step > 100 [stop]
fd :step
rt :angle
wait 3
spiral :step :angle + 10
end
Type
spiral 1 30
Well, can’t see much cuz it’s such a small step that doesn’t increase!
Type
spiral 10 30
spiral 30 30
spiral 10 5
CHANGE ANGLE TO +30
to spiral :step :angle
if :step > 100 [stop]
fd :step
rt :angle
wait 3
spiral :step :angle + 30
end
Type
spiral 40 5
AND OF COURSE YOU COULD CHANGE BOTH!
Nature, Spirals, Math, & Art
Navigate to the "Simple Beads" Page
AND
To the "Simple Beads" Procedure Pane
This page and procedure pane just show you how the beads are made.
Nature, Spirals, Math, & Art
Navigate to the "Spirals with Beads" Page
AND
To the "Spirals with Beads" Procedure Pane
Nature, Spirals, Math, & Art
SPIRALS WITH BEADS
to spiralA :step :angle
if :step > 80 [stop]
fd :step
rt :angle
stamp
wait 2
spiralA :step + 2 :angle
end
Type spiralA 2 20
But then put pd in there
tighten the spiral? How?
tighter angles
Type spiralA 2 30
Type spiralA 2 40
Type spiralA 2 300
Type spiralA 2 100
Change if :step >80 to >200
Type spiralA 10 75
Type spiralA 10 60
Type spiralA 10 45
Type spiralA 10 ????
Nature, Spirals, Math, & Art
Now change the angle!!!
to spiralB :step :angle
if :angle > 100 [stop]
stamp
fd :step
rt :angle
wait 1
spiralB :step :angle + 1
end
type spiralB 20 1
SPIRALC
to spiralC :step :angle
if :angle > 200 [stop]
stamp
fd :step
rt :angle
wait 1
spiralC :step :angle - 1
end
spiralC 50 90
Nature, Spirals, Math, & Art
Navigate to the "Dancing Spirals" Page
AND
To the "Dancing Spirals" Procedure Pane
PLAY!!!!