random walk converge to a goal

[tsh73]

We can easily split a picture with random walk.
But how to run it backwards to *assemble* picture with random walk?
Here's one of ways

(works in JB 1.01, JB 2 and LB 4.51 - because they all give same RND sequence after RANDOMIZE 0.5)

'how to make random walk converge to a goal?
'one of ways
'tsh73 Feb 2023
nomainwin

open "Randomly to a goal" for graphics_nsb_nf as #gr
#gr "home; down; posxy cx cy"
#gr "trapclose [quit]"

global sz, cx, cy
sz=30

nPts=4
dim x(nPts), y(nPts), colr$(nPts)
for i = 1 to nPts
   read x,y,c$
   'x(i)=x: y(i)=y: colr$(i)=c$    'forth pass
   x(i)=0-x: y(i)=0-y: colr$(i)=c$ 'back pass
next

dim dx(4), dy(4)    'directions
for i = 1 to 4
   read dx,dy
   dx(i)=dx: dy(i)=dy
next

randomize 0.5

'initial
for i = 1 to nPts
   call putBox x(i), y(i), colr$(i)
next
call pause 60

for k = 1 to 150    'just make sure thigs went off screen from initial pos
   for i = 1 to nPts
       scan
       dir = int(rnd(0)*4+1)
       call putBox x(i), y(i), "white"
       'print i, x(i),y(i),dx(dir), dy(dir)
       'x(i)=x(i)+dx(dir)  'forth pass
       'y(i)=y(i)+dy(dir)
       x(i)=x(i)-dx(dir)   'back pass
       y(i)=y(i)-dy(dir)
       call putBox x(i), y(i), colr$(i)
   next
   call pause 60
next

for i = 1 to nPts
   'redraw boxed on last position 'cause previous pos might obscure of of them
   call putBox x(i), y(i), colr$(i)
   'positions to be used in DATA
   print 0-x(i);",";0-y(i)
next
#gr "flush"


'r g
'b y

'back pass
data 0,-12, "yellow"
data 6,8, "red"
data 12,-1, "green"
data 3,-6, "blue"

'goal position - forth pass
'data 0, 0, "yellow"
'data -1, -1, "red"
'data 0, -1, "green"
'data -1, 0, "blue"

'directions
data 1,0, 0,1, -1,0, 0,-1

wait

[quit]
   timer 0
   close #gr
   end

sub putBox x, y, colr$
   #gr "color ";colr$
   #gr "backcolor ";colr$
   xx=cx+x*sz
   yy=cy+y*sz
   #gr "place ";xx; " "; yy
   #gr "boxfilled ";xx+sz; " "; yy+sz
end sub

sub pause mil
   t=time$("ms")+mil
   while time$("ms")<t
       scan
   wend
   exit sub
[quit]
   close #gr
   end
end sub


So the trick was
* start with goal,
* write ending coords,
* put them in DATA statement,
* and on back pass reverse the process (+ to - etc)

And for picture we need whole pre-garbled picture instead of DATA statements.