Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 09:25pm 02 Aug 2020 |
Here is a demo using turtle graphics, Each "slide" displays for 10 seconds.
'CMM2 Turtle Graphics Demo
'Adapted from various sources on the Internet
'by "Sasquatch"
Mode 1,8
Draw(400,45.5)
Pause(10000)
Draw (500,55.5)
Pause(10000)
Draw (600,60.2)
Pause(10000)
Draw (800,89.5)
Pause(10000)
Draw (900,110)
Pause(10000)
Draw (1000,119.9)
Pause(10000)
Draw (1000,120.1)
Pause(10000)
Draw (1000,135.1)
Pause(10000)
Draw (1000,145)
Pause(10000)
Draw (1000,176)
Pause(10000)
Draw (1000,190)
Pause(10000)
End
Sub Draw(Count,Angle)
Turtle Reset
N = 5
A = 90
For I = 1 To Count
Turtle Forward N
A = A + Angle
Turtle Heading A mod 360
Turtle Pen Colour Map(I mod 255)
N = N + 0.5
Next I
End Sub
'Adapted from various sources on the Internet
'by "Sasquatch"
Mode 1,8
Draw(400,45.5)
Pause(10000)
Draw (500,55.5)
Pause(10000)
Draw (600,60.2)
Pause(10000)
Draw (800,89.5)
Pause(10000)
Draw (900,110)
Pause(10000)
Draw (1000,119.9)
Pause(10000)
Draw (1000,120.1)
Pause(10000)
Draw (1000,135.1)
Pause(10000)
Draw (1000,145)
Pause(10000)
Draw (1000,176)
Pause(10000)
Draw (1000,190)
Pause(10000)
End
Sub Draw(Count,Angle)
Turtle Reset
N = 5
A = 90
For I = 1 To Count
Turtle Forward N
A = A + Angle
Turtle Heading A mod 360
Turtle Pen Colour Map(I mod 255)
N = N + 0.5
Next I
End Sub
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 09:26pm 02 Aug 2020 |
This one uses recursion instead of looping.
' Hilbert Curve using recursion
Mode 1,8
C = 1
Turtle Reset
Turtle Pen Up
Turtle Move 20,600
Turtle Pen Down
'Hilbert(Level,Angle,Length)
Hilbert(7,90,6)
Pause 10000
Turtle Reset
Turtle Pen Up
Turtle Move 150,550
Turtle Pen Down
Hilbert(8,90,2)
'Pause 10000
End
Sub Hilbert(Level,Angle,Length)
If Level = 0 Then Exit Sub
C = C + 0.1
Turtle Pen Colour Map(C Mod 255)
TurnTurtle(Angle)
Hilbert(Level - 1,0 - Angle, Length)
Turtle Forward Length
TurnTurtle(0 - Angle)
Hilbert(Level - 1,Angle,Length)
Turtle Forward Length
Hilbert(Level - 1,Angle,Length)
TurnTurtle(0 - Angle)
Turtle Forward Length
Hilbert(Level - 1,0 - Angle,Length)
TurnTurtle(Angle)
End Sub
Sub TurnTurtle(Angle)
If Angle > 0 Then
Turtle Turn Right Angle
Else If Angle < 0 Then
Turtle Turn Left Abs(Angle)
End If
End Sub
Mode 1,8
C = 1
Turtle Reset
Turtle Pen Up
Turtle Move 20,600
Turtle Pen Down
'Hilbert(Level,Angle,Length)
Hilbert(7,90,6)
Pause 10000
Turtle Reset
Turtle Pen Up
Turtle Move 150,550
Turtle Pen Down
Hilbert(8,90,2)
'Pause 10000
End
Sub Hilbert(Level,Angle,Length)
If Level = 0 Then Exit Sub
C = C + 0.1
Turtle Pen Colour Map(C Mod 255)
TurnTurtle(Angle)
Hilbert(Level - 1,0 - Angle, Length)
Turtle Forward Length
TurnTurtle(0 - Angle)
Hilbert(Level - 1,Angle,Length)
Turtle Forward Length
Hilbert(Level - 1,Angle,Length)
TurnTurtle(0 - Angle)
Turtle Forward Length
Hilbert(Level - 1,0 - Angle,Length)
TurnTurtle(Angle)
End Sub
Sub TurnTurtle(Angle)
If Angle > 0 Then
Turtle Turn Right Angle
Else If Angle < 0 Then
Turtle Turn Left Abs(Angle)
End If
End Sub
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 03:30am 03 Aug 2020 |
Recursive Fractal Trees!
' Recursive Fractal Trees
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,600
Turtle Pen Down
Tree(120)
End
Sub Tree(Length)
If Length < 1 Then Exit Sub
If Length > 20 Then
Turtle Pen Colour RGB(139,69,19)
Else
Turtle Pen Colour RGB(34,139,34)
EndIf
Turtle Pen Down
Turtle Forward Length
Turtle Turn Right 20
Tree(Length - 15)
Turtle Turn Left 40
Tree(Length - 15)
Turtle Pen UP
Turtle Turn Right 20
Turtle Backward Length
End Sub
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,600
Turtle Pen Down
Tree(120)
End
Sub Tree(Length)
If Length < 1 Then Exit Sub
If Length > 20 Then
Turtle Pen Colour RGB(139,69,19)
Else
Turtle Pen Colour RGB(34,139,34)
EndIf
Turtle Pen Down
Turtle Forward Length
Turtle Turn Right 20
Tree(Length - 15)
Turtle Turn Left 40
Tree(Length - 15)
Turtle Pen UP
Turtle Turn Right 20
Turtle Backward Length
End Sub
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 03:32am 03 Aug 2020 |
These Trees include a small amount of randomization making the trees look less uniform and more natural.
' Random Recursive Fractal Trees
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,600
Turtle Pen Down
For X = 1 to 5
Tree(100)
Pause(1000)
Next X
End
Sub Tree(Length)
If Length < 1 Then Exit Sub
Local RndLength = Length + Rnd * 5
Local RndAngle = 15 + Int(Rnd * 20.0)
If RndLength > 20 Then
Turtle Pen Colour RGB(139,69,19)
Else
Turtle Pen Colour RGB(34,139,34)
EndIf
Turtle Pen Down
Turtle Forward RndLength
Turtle Turn Right RndAngle
Tree(RndLength - 15)
Turtle Turn Left RndAngle * 2
Tree(RndLength - 15)
Turtle Pen UP
Turtle Turn Right RndAngle
Turtle Backward RndLength
End Sub
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,600
Turtle Pen Down
For X = 1 to 5
Tree(100)
Pause(1000)
Next X
End
Sub Tree(Length)
If Length < 1 Then Exit Sub
Local RndLength = Length + Rnd * 5
Local RndAngle = 15 + Int(Rnd * 20.0)
If RndLength > 20 Then
Turtle Pen Colour RGB(139,69,19)
Else
Turtle Pen Colour RGB(34,139,34)
EndIf
Turtle Pen Down
Turtle Forward RndLength
Turtle Turn Right RndAngle
Tree(RndLength - 15)
Turtle Turn Left RndAngle * 2
Tree(RndLength - 15)
Turtle Pen UP
Turtle Turn Right RndAngle
Turtle Backward RndLength
End Sub
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 03:47pm 03 Aug 2020 |
Sierpinski's Triangle Recursive Fractal. If you un-comment the pause statement, you will see that the entire thing is drawn as a series of tiny triangles.
' Sierpinski's Triangle Recursive Fractal
Mode 1,8
Colour 0,RGB(255,255,255)
Turtle Reset
Turtle Pen Up
Turtle Move 70,575
Turtle Turn Right 90
Turtle Pen Down
Turtle Pen Colour 0
Sierpinski(650,7)
End
Sub Sierpinski(Length,Level)
If Level = 0 Then
For i = 1 to 3
Turtle Forward Length
Turtle Turn Left 120
' Pause(50)
Next i
Exit Sub
EndIf
Sierpinski(Length / 2.0, Level - 1)
Turtle Pen Up
Turtle Forward Length / 2.0
Turtle Pen Down
Sierpinski(Length / 2.0, Level - 1)
Turtle Pen Up
Turtle Turn Left 120
Turtle Forward Length / 2.0
Turtle Turn Right 120
Turtle Pen Down
Sierpinski(Length / 2.0, Level - 1)
Turtle Pen Up
Turtle Turn Left 60
Turtle Backward Length / 2.0
Turtle Turn Right 60
Turtle Pen Down
End Sub
Mode 1,8
Colour 0,RGB(255,255,255)
Turtle Reset
Turtle Pen Up
Turtle Move 70,575
Turtle Turn Right 90
Turtle Pen Down
Turtle Pen Colour 0
Sierpinski(650,7)
End
Sub Sierpinski(Length,Level)
If Level = 0 Then
For i = 1 to 3
Turtle Forward Length
Turtle Turn Left 120
' Pause(50)
Next i
Exit Sub
EndIf
Sierpinski(Length / 2.0, Level - 1)
Turtle Pen Up
Turtle Forward Length / 2.0
Turtle Pen Down
Sierpinski(Length / 2.0, Level - 1)
Turtle Pen Up
Turtle Turn Left 120
Turtle Forward Length / 2.0
Turtle Turn Right 120
Turtle Pen Down
Sierpinski(Length / 2.0, Level - 1)
Turtle Pen Up
Turtle Turn Left 60
Turtle Backward Length / 2.0
Turtle Turn Right 60
Turtle Pen Down
End Sub
Guru
Joined: 11/12/2012
Location: United KingdomPosts: 10170
| Posted: 05:35pm 03 Aug 2020 |
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 05:50pm 03 Aug 2020 |
The Nautilus
' Square Nautilus Turtle Graphics Demo
Mode 1,8
Size = 275
N = 100
Angle = 10
Ratio = 0.97
Turtle Reset
For i = 1 to N
'Draw a square
For j = 1 to 4
Turtle Forward Size
Turtle Turn Left 90
Next j
'Rinse and Repeat
Turtle Turn Left Angle
Size = Size * Ratio
Next i
End
Mode 1,8
Size = 275
N = 100
Angle = 10
Ratio = 0.97
Turtle Reset
For i = 1 to N
'Draw a square
For j = 1 to 4
Turtle Forward Size
Turtle Turn Left 90
Next j
'Rinse and Repeat
Turtle Turn Left Angle
Size = Size * Ratio
Next i
End
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 07:03pm 03 Aug 2020 |
Here is a recursive fractal pine tree:
' Recursive Fractal Pine Trees
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,500
Turtle Pen Down
PineTree(100,20)
End
Sub PineTree(Length,Depth)
' Print Length
If Depth <= 0 Then Exit Sub
If Length > 2 Then
Turtle Pen Colour RGB(139,69,19) 'Make the sticks brown
Else
Turtle Pen Colour RGB(0,100,0) 'Make the needles Green
EndIf
Turtle Forward Length
PineTree(Length * 0.8, Depth - 1)
Turtle Turn Right 120
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 120
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 120
Turtle Pen Up
Turtle Backward Length
Turtle Pen Down
End Sub
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,500
Turtle Pen Down
PineTree(100,20)
End
Sub PineTree(Length,Depth)
' Print Length
If Depth <= 0 Then Exit Sub
If Length > 2 Then
Turtle Pen Colour RGB(139,69,19) 'Make the sticks brown
Else
Turtle Pen Colour RGB(0,100,0) 'Make the needles Green
EndIf
Turtle Forward Length
PineTree(Length * 0.8, Depth - 1)
Turtle Turn Right 120
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 120
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 120
Turtle Pen Up
Turtle Backward Length
Turtle Pen Down
End Sub
The second version includes a little randomization to make it less uniform
' Random Recursive Fractal Pine Trees
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,500
Turtle Pen Down
PineTree(100,19)
End
Sub PineTree(Length,Depth)
If Depth <= 0 Then Exit Sub
Local Angle = 110 + 20 * Rnd()
If Length > 5 Then
Turtle Pen Colour RGB(139,69,19) 'Make the sticks brown
Else
Turtle Pen Colour RGB(0,100,0) 'Make the needles Green
EndIf
Turtle Forward Length
PineTree(Length * 0.8, Depth - 1)
Turtle Turn Right Angle
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 120
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 240 - Angle
Turtle Pen Up
Turtle Backward Length
Turtle Pen Down
End Sub
Mode 1,8
Turtle Reset
Turtle Pen Up
Turtle Move 400,500
Turtle Pen Down
PineTree(100,19)
End
Sub PineTree(Length,Depth)
If Depth <= 0 Then Exit Sub
Local Angle = 110 + 20 * Rnd()
If Length > 5 Then
Turtle Pen Colour RGB(139,69,19) 'Make the sticks brown
Else
Turtle Pen Colour RGB(0,100,0) 'Make the needles Green
EndIf
Turtle Forward Length
PineTree(Length * 0.8, Depth - 1)
Turtle Turn Right Angle
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 120
PineTree(Length * 0.5, Depth - 3)
Turtle Turn Right 240 - Angle
Turtle Pen Up
Turtle Backward Length
Turtle Pen Down
End Sub
Guru
Joined: 07/08/2011
Location: AustraliaPosts: 6257
| Posted: 10:39pm 03 Aug 2020 |
Thank you for all the turtle demos.
It brings back memories of my brother demonstrating turtle drawing 50 years ago.
It was a new thing back then.
My brother went on to be a much better programmer than I will ever be.
Jim
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 11:29pm 03 Aug 2020 |
Ok, this one is basically blowing my poor little mind.
While it doesn't use Turtle Graphics it is a very interesting fractal known as the Barnsley Fern. I may "need" to do this one as a CSUB to see how fast it will fill. It would be interesting to zoom in if it would fill in faster.
'Barnsley's Fern
Mode 1,8
CLS
G = RGB(0,100,0)
For i = 1 to 1000000
Select Case Rnd()
Case IS < .01
NextX = 0
NextY = 0.16 * Y
Case .01 TO .08
NextX = .2 * X - .26 * Y
NextY = .23 * X + .22 * Y + 1.6
Case .08 TO .15
NextX = -.15 * X + .28 * Y
NextY = .26 * X + .24 * Y + .44
Case Else
NextX = .85 * X + .04 * Y
NextY = -.04 * X + .85 * Y + 1.6
End Select
X = NextX
Y = NextY
Pixel X * 100 + 400,600 - Y * 55 ,G
Next i
Mode 1,8
CLS
G = RGB(0,100,0)
For i = 1 to 1000000
Select Case Rnd()
Case IS < .01
NextX = 0
NextY = 0.16 * Y
Case .01 TO .08
NextX = .2 * X - .26 * Y
NextY = .23 * X + .22 * Y + 1.6
Case .08 TO .15
NextX = -.15 * X + .28 * Y
NextY = .26 * X + .24 * Y + .44
Case Else
NextX = .85 * X + .04 * Y
NextY = -.04 * X + .85 * Y + 1.6
End Select
X = NextX
Y = NextY
Pixel X * 100 + 400,600 - Y * 55 ,G
Next i
Guru
Joined: 29/01/2013
Location: CanadaPosts: 1126
| Posted: 11:51pm 03 Aug 2020 |
Turtle meets Dragon
This is perhaps my favorite fractal line drawing. Especially neat is the way they fit together. In this code, the red and green dragons are identical, just rotated 180 degrees. And they fit together perfectly.
It does look though that rounding errors are creeping into play here. The start point is fixed but the end point should also always end up the same. But if you watch closely between different orders, particularly the higher ones, the end point moves quite a lot. As a result, the green and red dragons must be the same order or they won't line up at all.
Orders higher than 19 don't work because the draw distance becomes less than 1 so nothing beyond a single dot gets drawn.
cls
turtle reset
text 100,500,"Dragon Curve - a Fractal","CT"
do
print @(0,520) "Order: (1-19)"
input "0 to quit: "; dord
loop until dord >= 0 and dord < 20
do
if dord = 0 then end
dord = dord - 1
dist = MM.HRES/2/(sqr(2)^dord)
cls
turtle reset
text 80, 0,"Dragon Curve","CT",2
text 80,20,"Order:" + str$(dord+1), "CT",2
turtle pen up ' no line yet
turtle move MM.HRES * .25, MM.VRES * .55
turtle pen down
turtle heading 90 - (dord MOD 8) * 45
turtle pen colour rgb(red)
DrawDragon(dord,1)
turtle heading 270 - (dord MOD 8) * 45
turtle pen colour rgb(green)
DrawDragon(dord,1)
do
print @(0,520) "Order: (1-19)"
input "0 to quit: "; dord
loop until dord >= 0 and dord < 20
loop
sub DrawDragon(ord, sig)
if ord = 0 then
turtle forward dist
else
DrawDragon(ord-1, 1)
turtle turn right 90 * sig
DrawDragon(ord-1, -1)
endif
end sub
turtle reset
text 100,500,"Dragon Curve - a Fractal","CT"
do
print @(0,520) "Order: (1-19)"
input "0 to quit: "; dord
loop until dord >= 0 and dord < 20
do
if dord = 0 then end
dord = dord - 1
dist = MM.HRES/2/(sqr(2)^dord)
cls
turtle reset
text 80, 0,"Dragon Curve","CT",2
text 80,20,"Order:" + str$(dord+1), "CT",2
turtle pen up ' no line yet
turtle move MM.HRES * .25, MM.VRES * .55
turtle pen down
turtle heading 90 - (dord MOD 8) * 45
turtle pen colour rgb(red)
DrawDragon(dord,1)
turtle heading 270 - (dord MOD 8) * 45
turtle pen colour rgb(green)
DrawDragon(dord,1)
do
print @(0,520) "Order: (1-19)"
input "0 to quit: "; dord
loop until dord >= 0 and dord < 20
loop
sub DrawDragon(ord, sig)
if ord = 0 then
turtle forward dist
else
DrawDragon(ord-1, 1)
turtle turn right 90 * sig
DrawDragon(ord-1, -1)
endif
end sub
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 12:12am 04 Aug 2020 |
That is a nice one! At lower orders it doesn't give any clue as to it's potential. It amazes me how such a simple looking algorithm can generate something so complex.
Thanks for sharing, if you have any other gems I'd like to see them.
Guru
Joined: 30/06/2020
Location: AustraliaPosts: 341
| Posted: 12:46am 04 Aug 2020 |
Cool thread, there's some other recursive line fractals I'd like to try if I get time (I think I was inspired by one called the koch curve and I changed things around and got a new one with a kind of hexagonal pattern)
Guru
Joined: 30/06/2020
Location: AustraliaPosts: 341
| Posted: 01:32am 04 Aug 2020 |
Cool thread, there's some other recursive line fractals I'd like to try if I get time (I think I was inspired by one called the koch curve and I changed things around and got a new one with a kind of hexagonal pattern).
Update:
I gave it a quick try by modifying the Sierpinski program above. The rounding errors were already spoiling it before I got as much detail as I wanted. Here's the code I used:
' Hex Gasket Recursive Fractal
Mode 1,8
Colour 0,RGB(255,255,255)
Turtle Reset
Turtle Pen Up
Turtle Move 70,575
Turtle Turn Right 90
Turtle Pen Down
Turtle Pen Colour 0
'Gasket(650,7)
Gasket(650,5)
End
Sub Gasket(Length,Level)
If Level = 0 Then
Turtle Forward Length
' Pause(50)
Exit Sub
EndIf
Turtle Pen Up
Turtle Forward Length
Turtle Pen Down
Turtle Turn Left 120
Gasket(Length / 2.0, Level - 1)
Turtle Turn Left 60
Gasket(Length / 2.0, Level - 1)
Turtle Turn Left 60
Gasket(Length / 2.0, Level - 1)
Turtle Turn Left 120
Turtle Pen Up
Turtle Forward Length
Turtle Pen Down
End Sub
I changed the program to exactly retrace the same lines when going backwards, rather than taking a shortcut. It's more complicated, but it cancels out the rounding errors:
' Hex Gasket Recursive Fractal
Mode 1,8
Colour 0,RGB(255,255,255)
Turtle Reset
Turtle Pen Up
Turtle Move 70,575
Turtle Turn Right 90
Turtle Pen Down
Turtle Pen Colour 0
'Gasket(650,7)
Gasket(650,10)
End
Sub Gasket(Length,Level)
If Level = 0 Then
Turtle Forward Length
Turtle Pen Up
Turtle Backward Length
Turtle Pen Down
' Pause(50)
Exit Sub
EndIf
Turtle Turn Left 60
Turtle Pen Up
Turtle Forward Length/2
Turtle Pen Down
Turtle Turn Right 180
Gasket(Length / 2.0, Level - 1)
Turtle Turn Left 180
Turtle Turn Right 60
Turtle Pen Up
Turtle Forward Length/2
Turtle Pen Down
Turtle Turn Right 180
Gasket(Length / 2.0, Level - 1)
Turtle Turn Left 180
Turtle Turn Right 60
Turtle Pen Up
Turtle Forward Length/2
Turtle Pen Down
Turtle Turn Right 180
Gasket(Length / 2.0, Level - 1)
Turtle Turn Left 180
Turtle Pen Up
Turtle Turn Right 180
Turtle Forward Length/2
Turtle Turn Left 60
Turtle Forward Length/2
Turtle Turn Left 60
Turtle Forward Length/2
Turtle Turn Right 60
Turtle Turn Right 180
Turtle Pen Down
End Sub
Guru
Joined: 08/05/2020
Location: United StatesPosts: 377
| Posted: 03:53am 04 Aug 2020 |
Good Job! MMBasic does make it easy to try changes quickly. I've added this one to my collection as well.
Guru
Joined: 18/11/2011
Location: United KingdomPosts: 4026
| Posted: 08:21am 04 Aug 2020 |
Just in case anyone doesn't know, each dragon is the same as folding a piece of paper in half repeatedly (you can't do it much as it gets too thick) then opening it out so every crease is a right angle and viewing from an edge side.
Origami...
John
Senior Member
Joined: 04/07/2020
Location: United KingdomPosts: 134
| Posted: 04:38pm 04 Aug 2020 |
Wow, these are awesome. I love seeing these patterns drawing and stuff. Before I got my CMM2, I played around in QBASIC 1 in DOS, and made this
https://www.youtube.com/watch?v=zJe2Ajp2eVg
Keep em coming!
Guru
Joined: 20/06/2011
Location: AustraliaPosts: 2947
| Posted: 06:57am 05 Aug 2020 |
Hi Pete,
That code fails for anything after Option 3.. I think it is to do with negative angles.
Maybe something changed in a later version of MMBasic, I am using 5.05.04
There is also an error in the Barnsley Fern by sasqatch.
Kind Regards
Mick
Guru
Joined: 07/08/2011
Location: AustraliaPosts: 6257
| Posted: 07:11am 05 Aug 2020 |
Yep. All fixed in the latest beta.
Jim
Guru
Joined: 20/06/2011
Location: AustraliaPosts: 2947
| Posted: 10:02am 05 Aug 2020 |
Thanks Jim,
I thought it was firmware differences, I will try the latest beta..
I usually stick to the latest release version
Regards,
Mik