Hermann Grid

- optical illusion

First noted by Hermann in 1870. The yellow dots at each junction appear to flash or scintillate when you move your eyes over the grid.
Two sets of grid tiles are drawn, background dark squares, and yellow dots.
Try other Order values from 1 to 14...

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
  For (List " Col 1 : Order ) [
    For (List " Row 1 : Order ) [
      SetXY : Side *( : Col - : Offset ) : Side *( : Row - : Offset )
      Tile : Col : Row : Side ] ]
End

To Tile : Col : Row : Side
  SetPC [33 0 58] SetPW 1 Square 0.8* : Side Fill Wait 1
  If And : Col >1 : Row >1 [
    Back : Side /2 Right 90 Back : Side /2 Left 90
    SetPC Yellow SetPW 0.2* : Side Dot Pos Wait 1]
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

To Go : Order
  New SetSC [121 87 39]
  Make " Side Int (418/( : Order +1))
  GridSq : Order +1 : Side
End

Here is a Hermann spiral illusion. Stare at the centre and you will see concentric dark rings where the radiating lines cross.

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

To Curve : Parity
  # draw curved line
  PenDown Repeat 11 [
    SetPW RepCount/1.8
    Forward 20 Right :Parity *(RepCount+5) ]
  Forward 3 PenUp
End

To Go
  New SetSC [0 0 32] SetPC [196 255 255]
  Repeat 36 [
    Home Right 10*RepCount Curve 1
    Home Left 10*RepCount Curve Minus 1]
End

Hermann Grid
Hermann Grid

 

Hermann Grid
Hermann Spiral

Procedures blue
Variables pink
Comments green
Library gray