Logo Arts

"merging the arts of programming and graphics"

Tile

- random patterns

A geometric tile pattern is formed when individual square tiles are fitted together in an array. Each tile can have 4 random rotations, with a color assigned to each. Most tiles are simple shapes that tile together well.
Some tiles could also be drawn as a mirror image. They are not used in this program, so no tiles are 'turned over'.

Enter GoX for a series of random patterns.
Enter Go Pattern Order to draw a particular pattern.

To New
# set default screen, pen and turtle values
ResetAll SetScreenSize [400 400] HideTurtle
SetSC Black SetPC Green SetPS 1 PenUp
End

To GridSq :Order :Side
# draw tile at each column x row position
LocalMake "Offset (1+:Order)/2
LocalMake "Ps [] LocalMake "Total :Order*:Order
Repeat :Total [Make "Ps LPut RepCount :Ps]
Repeat :Total [
LocalMake "P Pick :Ps
LocalMake "Ps Remove :P :Ps
LocalMake "Col 1+Mod :P-1 :Order
LocalMake "Row 1+Int (:P-1)/:Order
SetXY :Side*(:Col-:Offset) :Side*(:Row-:Offset)
Tile :Col :Row :Side]
End

To Tile :Col :Row :Side
# use global value of :Tile to draw selected tile
SetH Pick [0 90 180 270] # tile rotation
SetPC Item (1+Heading/90) [1 2 3 6]
# SetPC Pick [1 2 3 6] # comment in for random color
# SetPC :FlatCol # comment in for all one color
GlobalMake "Hue PenColor
Run Se (Word "Tile :TileNo) 0.95*:Side
End

To Tile1 :Side
Left 45 Arch 270 :Side/2 Right 45 Back :Side/2
PenDown Forward :Side/2 Right 90 Forward :Side/2
PenUp Back 3*:Side/4 SetPC Dark PenColor Fill
SetPC :Hue Forward :Side/2 Left 90 Arch 180 :Side/4
Forward :Side/8 SetPC Dark Dark PenColor Fill
End

To Tile2 :Side
Right 45 Kite 1.414*:Side
SetPC Dark PenColor Fill PenUp SetPC :Hue
Right 45 Forward :Side/2 Left 153.4
PenDown Forward :Side /2.7 Right 36.8 Forward :Side /2.7 PenUp
Right 150 Forward :Side/4
SetPC Dark Dark PenColor Fill
End

To Tile3 :Side
Right 45 Back 1.414*:Side/4 RightAngTri 1.414*:Side
SetPC Dark PenColor Fill SetPC :Hue
Right 45 Forward :Side/8 RightAngTri :Side/2
SetPC Dark Dark PenColor Fill
End

To Tile4 :Side
Right 45 Lens 1.414*:Side Left 45
SetPC Dark PenColor Fill
SetPC :Hue Lens :Side/1.38
SetPC Dark Dark PenColor Fill
End

To Tile5 :Side
Right 45 Back 1.414*:Side/2
SetPC Yellow SetPW :Side/10 Arch 90 :Side/2
Right 45 SetPW 1 SetPC :FlatCol SetPC Dark PenColor
PenDown Repeat 4 [
Forward :Side/4 PenUp Forward :Side/2 PenDown
Forward :Side/4 Left 90]
PenUp Forward :Side/2 Left 90 Forward :Side/2
Repeat 2 [
Back :Side/2 Arch 180 :Side/4
Back :Side/2 Arch 68 0.9*:Side Forward :Side
Back :Side/6 FillZone Forward :Side/6 Left 180]
SetPC :FlatCol Repeat 2 [
Back :Side/2 Arch 180 :Side/4
Back :Side/2 Arch 68 0.9*:Side Forward :Side Left 180]
Left 135 Back 1.414*:Side/2
SetPC Yellow SetPW :Side/10 Arch 90 :Side/2 SetPW 1
End

To Tile6 :Side
SetPC :FlatCol Back :Side/6 Left 90 PenDown
Forward :Side/2 Left 90 Forward :Side/3
Left 90 Forward :Side Left 90
Forward :Side/3 Left 90 Forward :Side/2
PenUp Forward :Side/6 Right 90 Back :Side/6
SetPC Dark PenColor Fill Forward :Side/6
SetPC Yellow PenDown Forward :Side/6 PenUp
Forward :Side/6 Circle :Side/6 SetPC Orange Fill
End

To Tile7 :Side
If Or (Heading =90) (Heading=270) [Right 26.5] [Right 63.5]
Square 0.74*:Side Back 0.37*:Side PenDown
Forward 0.37*:Side Right 90 Forward 0.37*:Side
PenUp Back :Side/2 SetPC Dark PenColor Fill
Right 30 Forward :Side/3
SetPC Dark PenColor Fill
End

To Tile8 :Side
Chevron :Side Chevron :Side/2
Forward 3*:Side/8 SetPC Dark PenColor Fill
Back :Side/4 SetPC Dark PenColor Fill
End

To Tile9 :Side
Right 45 Back 1.414 *:Side/6 Left 45 Square 2*:Side/3
SetPC Dark PenColor Fill SetPC :Hue
Forward :Side/3 PenDown Forward :Side/3
Right 45 Back 1.414 *:Side/3 PenUp Forward 1.414 *:Side/3
PenDown Right 45 Forward 2*:Side/3 Right 90 Forward 2*:Side/3
Right 45 Forward 1.414 *:Side/3 PenUp
Right 135 Forward 2*:Side/3 Right 45 PenDown Forward 1.414 *:Side/3
PenUp Right 135 Forward :Side/6 Right 90 Forward :Side/12
SetPC Dark Dark PenColor Fill Forward 2*:Side/3 Fill
Back :Side/6 SetPC Dark PenColor Fill
End

To Tile10 :Side
Back :Side/2 Right 90 Back :Side/2
PenDown Forward :Side Left 90 Forward :Side
Left 90 Forward :Side/3 Left 90 Forward 2*:Side/3
Right 90 Forward 2*:Side/3 Left 90 Forward :Side/3
PenUp Back :Side PenDown Repeat 4 [
Forward :Side/3 Left 90] PenUp
Left 45 Forward 1.414*:Side/6 SetPC Dark Dark PenColor Fill
Forward 2*1.414*:Side/3 SetPC :Hue SetPC Dark PenColor Fill
End

To Tile11 :Side
Right 90 Forward :Side/3 Left 90 Forward :Side/6
Repeat 2 [
SetPC Dark Dark PenColor
FillPolygon [PD (Pgram :Side/3 2*:Side/3 Minus 1)]
SetPC :Hue (Pgram :Side/3 2*:Side/3 Minus 1)
Left 90 Forward :Side/2 Left 90
SetPC Dark PenColor FillPolygon [PD Pgram 2*:Side/3 2*:Side/3]
SetPC :Hue Pgram 2*:Side/3 2*:Side/3
Right 90 Forward :Side/6 Left 90 Forward :Side/3]
End

To Tile12 :Side
Left 90 Forward :Side/4 Right 90 Forward :Side/4
Repeat 2 [
SetPC Dark Dark PenColor FillPolygon [PD Pgram :Side/2 :Side/2]
SetPC :Hue Pgram :Side/2 :Side/2 Right 90 Forward :Side/2 Right 90
SetPC Dark PenColor FillPolygon [ PD (Pgram :Side/2 :Side/2 Minus 1)]
SetPC :Hue (Pgram :Side/2 :Side/2 Minus 1) Forward :Side/2]
End

To GoX
Forever [Go (1+Random 12) (4+Random 5) Wait 240]
End

To Go :Tile :Order
New Make "Side Int 380/:Order # screen width 380
GlobalMake "TileNo :Tile
GlobalMake "FlatCol Pick [4 6 9 15] # flat color for tiles 5 and 6
If :Order<6 [SetPW Abs (7-:Order)] # fat pen for low orders
GridSq :Order :Side
End

To Arch :Angle :Radius
# symmetrical arc drawn relative to turtle heading
Arc :Radius Heading-:Angle/2 Heading+:Angle/2
End

To Chevron :Size
# chevron shape drawn from centre (tp)
Make "Offset :Size/4 # global offset fill
PenDown Left 45
Forward 1.414*:Size/2 Right 135 Forward :Size/2
Right 45 Forward 1.414*:Size/2 Right 90 Forward 1.414*:Size/2
Right 45 Forward :Size/2 Right 135 Forward 1.414*:Size/2
Left 45 PenUp
End

To Kite :Size
# kite shape drawn from centre (tp)
Back :Size/2 PenDown
Left 18.4 Forward :Size/1.26 Right 63.4
Forward :Size/2.82 Right 90 Forward :Size/2.82
Right 63.4 Forward :Size/1.26
PenUp Right 161.6 Forward :Size/2 # return to centre
End

To Lens :Size
# lens shape drawn from centre (tp)
Repeat 2 [
Back :Size/2 Arch 90 :Size/1.414
Forward :Size/2 Left 180]
End

To Pgram :Wide :High [:P 1]
# parallelogram shape drawn from centre (tp)
# default parity of 1, use minus 1 for mirror image
LocalMake "Ang ATan :Wide/(:High/2) # inner angle
LocalMake "Len :Wide/ Sin :Ang # side length
Back :High/4 Right :P*:Ang Back :Len/2 PenDown
Repeat 2 [
Forward :Len Left :P*:Ang Forward :High/2 Left :P*(180-:Ang)]
PenUp Forward :Len/2 Left :P*:Ang Forward :High/4 # r2c
End

To RightAngTri :Size
# right angled triangle drawn from centre (tp)
Back :Size/4 Right 45
PenDown Forward 1.414*:Size/2
Left 135 Forward :Size
Left 135 Forward 1.414*:Size/2 PenUp
Left 135 Forward :Size/4 # return to centre
End

To Square :Side
# square (side x side) drawn from centre (tp)
Back :Side/2 Right 90 Back :Side/2 PenDown
Repeat 4 [
Forward :Side Left 90]
PenUp Forward :Side/2 Left 90 Forward :Side/2 # r2c
End