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Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 09:25pm 02 Aug 2020

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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

-Carl

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 09:26pm 02 Aug 2020

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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

-Carl

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 03:30am 03 Aug 2020

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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

-Carl

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 03:32am 03 Aug 2020

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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

-Carl

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 03:47pm 03 Aug 2020

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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

-Carl

matherp
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Joined: 11/12/2012
Location: United Kingdom
Posts: 8815

Posted: 05:35pm 03 Aug 2020

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Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 05:50pm 03 Aug 2020

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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

-Carl

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 07:03pm 03 Aug 2020

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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

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

-Carl

TassyJim

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Joined: 07/08/2011
Location: Australia
Posts: 6006

Posted: 10:39pm 03 Aug 2020

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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

VK7JH
MMedit MMBasic Help

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 11:29pm 03 Aug 2020

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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

-Carl

vegipete

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Joined: 29/01/2013
Location: Canada
Posts: 1099

Posted: 11:51pm 03 Aug 2020

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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

Visit Vegipete's *Mite Library for cool programs.

Sasquatch

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Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 12:12am 04 Aug 2020

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vegipete said 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.

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.

-Carl

capsikin
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Joined: 30/06/2020
Location: Australia
Posts: 341

Posted: 12:46am 04 Aug 2020

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capsikin
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Joined: 30/06/2020
Location: Australia
Posts: 341

Posted: 01:32am 04 Aug 2020

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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:

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

Sasquatch

Guru

Joined: 08/05/2020
Location: United States
Posts: 324

Posted: 03:53am 04 Aug 2020

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capsikin said 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)

Good Job! MMBasic does make it easy to try changes quickly. I've added this one to my collection as well.

-Carl

JohnS
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Joined: 18/11/2011
Location: United Kingdom
Posts: 3737

Posted: 08:21am 04 Aug 2020

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Sasquatch said

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

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

Atomizer_Zero
Senior Member

Joined: 04/07/2020
Location: United Kingdom
Posts: 134

Posted: 04:38pm 04 Aug 2020

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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!

bigmik

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Joined: 20/06/2011
Location: Australia
Posts: 2906

Posted: 06:57am 05 Aug 2020

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vegipete said Turtle meets Dragon

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

Mick's uMite Stuff can be found >>> HERE (Kindly hosted by Dontronics) <<<

TassyJim

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Joined: 07/08/2011
Location: Australia
Posts: 6006

Posted: 07:11am 05 Aug 2020

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bigmik said
Maybe something changed in a later version of MMBasic, I am using 5.05.04

Mick

Yep. All fixed in the latest beta.

Jim

VK7JH
MMedit MMBasic Help

bigmik

Guru