Pursuit curves are formed when one object chases after another, for instance a dog after a rabbit.
In this program a number of turtles are created round the edge of a circle.
Each turtle faces the turtle on it's immeadiate left. Then each one in
turn steps towards its target. As the target turtle is also moving an
inward spiral or pursuit curve results.
The program halts when the turtles reach the centre.
# set default screen, pen and turtle values
ResetAll SetScreenSize [400 400] HideTurtle
SetSC Black SetPC Green SetPS 1 PenUp
To Init :N
If :N <2 [Print [Need more than one turtle!] Stop]
Repeat :N [
Make "Angle RepCount*360/:N
SetPC Hue :Angle PenUp
Make "Dist 190 If :N=4 [Make "Dist 260] If :N=8 [Make "Dist 200]
Left 180/:N +:Angle Back :Dist PenDown]
To Hue :Theta
# Output RGB hue list from angle :Theta
Make "Red Round 127.5*(1+Sin :Theta)
Make "Green Round 127.5*(1+Sin (:Theta+120))
Make "Blue Round 127.5*(1+Sin (:Theta+240))
Output (List :Red :Green :Blue)
To Go :N
New SetTurtlesMax :N+1 Init :N
Make "Count 0
While [(Distance [0 0]) >2] [
Repeat :N [
SetTurtle RepCount Make "myPos Pos
If RepCount+1 >:N
[SetTurtle 1] [SetTurtle RepCount+1]
If :Count=Integer :Count
[Make "thisPos Pos SetPos :myPos SetPos :thisPos]
[SetH Towards :myPos Forward 2 Wait 1] ]
Make "Count :Count+0.1]
To run, enter go 4, go 7 etc for increasing number of turtles.