Brain challenge: The black hole.

[plus]

every point is a distance and an angle from another point, here we measure from center of black hole cx, cy.

dx = cx - sx(i): dy = cy - sy(i)
d = (dx * dx + dy * dy) ^ .5

dx = distance (and direction) an x is from the center x coordinate
dy = distance (and direction) an y is from the center y coordinate

d = magnitude of the distance (no direction) the point x, y is from the point cx, cy the center of screen and origin of Black Hole.

b = Atan2(dy, dx)
b = the angle of point x, y to the center cx,cy of the black hole.

the angle a is constantly increasing with every loop adding a to b here
newX = cx + d * cos(a + b)
newY = cy + d * sin(a + b)
swings the x, y point around the center of the Black Hole by angle a added to the angle it was b.

Hope this helps with understanding.

Oh also, Atan2 is read as "the Angle whose tangent is dy/dx" so for the function Atan2 list dy first and dx 2nd.
ie if the tangent = some ratio then the Angle to have that was Atan2(dy, dx)

sin cos tan... are all ratios unique to particular angles of right triangles upon which trig is based.

b = b + ...

[honky]

Thank you "plus", I record your explanations and I study your code with it.

Hey, "plus" is a French word, Google Trad tells me "More",

Why a French word on an English-speaking forum ?

[plus]

plus means more or additionally in English too, my original avatar name was B+ like a grade you get from school = paper, essay or test was good but not outstanding

b = b + ...

[honky]

I put A without hesitation

[Rod]

Well this is Rod's contribution. You need to let it run for a while to form the Accretion disk. The star is a data object that has angle and radius as well as x and y so we lose a lot of the maths in forming the spiral. Reduce the number of stars if it is overwhelming your PC.

   'PRESS Q TO QUIT
   'set up a full screen display
   'the same size as the users screen
   nomainwin
   WindowWidth=DisplayWidth
   WindowHeight=DisplayHeight
   graphicbox #w.gb,0,0,WindowWidth,WindowHeight
   open "Starfield" for window_popup as #w
   #w "trapclose [quit]"
   #w.gb "down"

   'set our centre
   cx=int(WindowWidth/2)
   cy=int(WindowHeight/2)

   'create background for the universe
   #w.gb "fill 96 96 96 ; size 2"
   for r=1 to int(WindowWidth/2)
       #w.gb "place ";cx;" ";cy;" ; circle ";r
       #w.gb "color ";0+r*.1;" ";0+r*.1;" ";0+r*.1
   next

   'set up for xor drawing
   #w.gb "color red"
   #w.gb "rule xor"

   'dim our star object and index values
   dim star(1000,6)
   angle=1
   radius=2
   size=3
   xpos=4
   ypos=5

   'create first set of stars
   for s = 1 to 1000
       star(s,angle) = int(rnd(0)*360)
       star(s,radius) = int(rnd(0)*DisplayWidth)+500
       star(s,size) = int(rnd(0)*3)+1
       star(s,xpos) = cx-(star(s,radius)*sin(star(s,angle)/57.29577951))
       star(s,ypos) = cy-(star(s,radius)*cos(star(s,angle)/57.29577951))
       #w.gb "size ";star(s,size);" ; set ";star(s,xpos);" ";star(s,ypos)
   next

   'set up an event to look for key presses
   #w.gb "when characterInput [stop]"
   #w.gb "setfocus"

[move]
   for s= 1 to 1000
       #w.gb "size ";star(s,size);" ; set ";star(s,xpos);" ";star(s,ypos)
       star(s,radius)=int(star(s,radius)*.9)
       star(s,angle)=star(s,angle)+3 mod 360
       star(s,xpos) = cx-(star(s,radius)*sin(star(s,angle)/57.29577951))
       star(s,ypos) = cy-(star(s,radius)*cos(star(s,angle)/57.29577951))
       #w.gb "size ";star(s,size);" ; set ";star(s,xpos);" ";star(s,ypos)

       if star(s,radius)<25 then
           #w.gb "size ";star(s,size);" ; set ";star(s,xpos);" ";star(s,ypos)
           star(s,angle) = int(rnd(0)*360)
           star(s,radius) = int(rnd(0)*DisplayWidth)+25
           star(s,size) = int(rnd(0)*3)+1
           star(s,xpos) = cx-(star(s,radius)*sin(star(s,angle)/57.29577951))
           star(s,ypos) = cy-(star(s,radius)*cos(star(s,angle)/57.29577951))
           #w.gb "size ";star(s,size);" ; set ";star(s,xpos);" ";star(s,ypos)
       end if
   scan
   next
   goto [move]


[stop]
   timer 0
   w$=right$(Inkey$,1)
   if w$ = "q" then [quit]
   wait

[quit]
   timer 0
   close #w
   end




Attachments:

[tsh73]

Ahhh, soo many good programs! ;)

Re: Honky's unrealistic colors
Well, they might be not that realistic
but it really
.          really
.              really
feels like old (good) Spectrum days...

Re: Separate glittering ring of stars of B+
Clever!
Also, colors are nice.

Re: Rod's 1000-stars galaxy
Looks really nice
and FAST
How you did that? There your CLEAR code?
Ah, that's one XOR!
Commenting out XOR reveals hidden warp tunnel, have a look!
;)
I found kind of problem, though
Pressing any key pauses (stops) simulation

Here's last part of program mod, that quits only on "q", and pretty much ignores everything else
       end if
   next
   scan   'scan after next, so no jumps out of loop
   goto [move]


[stop]
   w$=right$(Inkey$,1)
   if w$ = "q" then timer 0: goto [quit]  'only 'q' quits
   goto [move]  'else go where SCAN was, to the next iteration

[quit]
   timer 0
   close #w
   end


[tsh73]

I got the idea a few days ago -
what will happen if star will travel not to hole center,
but to tangential point on an accretion circle?

(But how to get the math right?)
So to do it I pasted whole vector library
(and spent extra evening debugging it.
Happens that as now it NEEDS global "pi" variable, atan2 and vectRotate$ do really wierd thing without it.)

But I like what I got
stars go tangential - they get sprinning naturally, without any extra +a
And looks like they go in spirals closing to R circle
(probably never hitting it)
but then I set condition to
If d < R+0.001 Then
it (mostly) makes several spins around and then passes - to be created outside with
call newStar i

So now stars are attracted to the circle, rotate counterclockwize
(you can change to clockwize with vec2$=vectRotate$(vec1$,0-asn(R/d)))
eventually pass event horison ( ;) ) If d < R+0.001 Then
and get reborn outside!

global H$, XMAX, YMAX
H$ = "gr"
Xmax = 600 '<======================================== actual drawing space needed
Ymax = 600 '<======================================== actual drawing space needed
global pi 'needs to be here for vector library to work
pi = acs(-1)

nomainwin

WindowWidth = Xmax + 8
WindowHeight = Ymax + 32
UpperLeftX = (DisplayWidth - Xmax) / 2  'or delete if XMAX is 1200 or above
UpperLeftY = (DisplayHeight - Ymax) / 2   'or delete if YMAX is 700 or above

open "Black Hole Attractor" for graphics_nsb_nf as #gr
#gr "trapclose quit"
#gr "size 1"
#gr "down"
#gr "fill 60 0 30"

nstars = 100
'nstars = 60
'nstars = 200
Dim sx(nstars), sy(nstars), sr(nstars)
cx = 300: cy = 300
'setup start stars
For i = 1 To nstars
   sx(i) = Rnd(0) * 600
   sy(i) = Rnd(0) * 600
   sr(i) = Rnd(0) * 3 + 1
Next
R=50
R=30
R=40
Do
#gr "discard"
   #gr "fill 60 0 30"
   'show stars
   #gr "color 200 200 200"
   #gr "backcolor 255 255 255"

   For i = 1 To nstars
       vec1$=vect$(cx-sx(i),cy-sy(i))
d = vectLen(vec1$)
'black hole radius
       'If d < R+1 Then
If d < R+0.001 Then 'so it is slow spiral, and eventually pass
           call newStar i
else
'draw
#gr "place ";sx(i);" ";sy(i);"; circlefilled ";sr(i)
'now update stars falling into black hole
' get point on tangential line instead
'vec1$=vect$(cx-sx(i),cy-sy(i)) 'line to center
'alpha=asn(R/vectLen(vec1$)) 'angle of tangential line
'alpha=asn(R/d)
vec2$=vectRotate$(vec1$,asn(R/d))
'dx = cx - sx(i): dy = cy - sy(i)
'dx = val(word$(vec2$,1)) 'so goal point is not center but point on tangential line
dx = val(vec2$) 'shorcut: val returns what it could read
dy = val(word$(vec2$,2))
' move it
dx = R * dx / (d * d)
dy = R * dy / (d * d)
sx(i) = sx(i) + dx
sy(i) = sy(i) + dy
end if
   Next
'wait
   '#gr "color 128 0 0"
   '#gr "backcolor 0 0 0"
   '#gr "place ";cx;" ";cy;"; circlefilled ";R
   call pause 30
Loop until something


Sub newStar i
   r = Int(Rnd(0) * 4) ' 0 to 3
   Select Case r
       Case 0
           sx(i) = Rnd(0) * 600
           sy(i) = 0
       Case 1
           sx(i) = Rnd(0) * 600
           sy(i) = 599
       Case 2
           sy(i) = Rnd(0) * 600
           sx(i) = 0
       Case 3
           sy(i) = Rnd(0) * 600
           sx(i) = 599
   End Select
End Sub

sub quit H$
   close #gr
   end
end sub

sub pause mil   'tsh version has scan built-in
   t0 = time$("ms")
   while time$("ms") < t0 + mil : scan : wend
end sub

'---------------------------------------------

function vect$(x,y)
   vect$=x;" ";y
end function

function vectX(v$)
   vectX=val(word$(v$,1))
end function

function vectY(v$)
   vectY=val(word$(v$,2))
end function

function vectLen(v$)
   x=val(word$(v$,1))
   y=val(word$(v$,2))
   vectLen=sqr(x*x+y*y)
end function

function vectUnit$(v$)
   x=val(word$(v$,1))
   y=val(word$(v$,2))
   vectLen=sqr(x*x+y*y)
   vectUnit$=x/vectLen;" ";y/vectLen
end function

function vectAdd$(v1$,v2$)
   x1=val(word$(v1$,1))
   y1=val(word$(v1$,2))
   x2=val(word$(v2$,1))
   y2=val(word$(v2$,2))
   vectAdd$=x1+x2;" ";y1+y2
end function

function vectSub$(v1$,v2$)
   x1=val(word$(v1$,1))
   y1=val(word$(v1$,2))
   x2=val(word$(v2$,1))
   y2=val(word$(v2$,2))
   vectSub$=x1-x2;" ";y1-y2
end function

function vectDotProduct(v1$,v2$)
   x1=val(word$(v1$,1))
   y1=val(word$(v1$,2))
   x2=val(word$(v2$,1))
   y2=val(word$(v2$,2))
   vectDotProduct=x1*x2+y1*y2
end function

function vectScale$(a,v$)   'a * vector v$
   x=val(word$(v$,1))
   y=val(word$(v$,2))
   vectScale$=a*x;" ";a*y
end function

function vectTangent$(v$,base$)
   n$=vectUnit$(base$)
   vectTangent$=vectScale$(vectDotProduct(n$,v$),n$)
end function

function vectNorm$(v$,base$)
   vectNorm$=vectSub$(v$,vectTangent$(v$,base$))
end function

function vectAngle(v$)
   x=val(word$(v$,1))
   y=val(word$(v$,2))
   vectAngle=atan2(y,x)
end function

function vectFromPolar$(rho, phi)
   vectFromPolar$=rho*cos(phi);" ";rho*sin(phi)
end function

function vectRotate$(v$,alpha)
   x=val(word$(v$,1))
   y=val(word$(v$,2))
   rho=sqr(x*x+y*y)
   phi=atan2(y,x)+alpha
   vectRotate$=rho*cos(phi);" ";rho*sin(phi)
end function

function dePi$(x)   'pure aestetics
   'dePi$=x/pi;"Pi"
   dePi$=using("##.###",x/pi);"Pi" 'place for sign
end function

function normalizeAngle(x)
   x=x mod (2*pi)
   if x <0 then x=x+(2*pi)
   normalizeAngle = x
end function

function dePiNorm$(x)   'pure aestetics
   'norm z first
   x=x mod (2*pi)
   if x <0 then x=x+(2*pi)
  dePiNorm$=using("##.###",x/pi);"Pi"
end function


'---------------------------
function atan2(y,x)
   'pi = asn(1) * 2    'global
   if x <> 0 then arctan = atn(y/x)

   select case
       case x > 0
       atan2 = arctan

       case y>=0 and x<0
       atan2 = pi + arctan

       case y<0 and x<0
       atan2 = arctan - pi

       case y>0 and x=0
       atan2 = pi / 2

       case y<0 and x=0
       atan2 = pi / -2
   end select
end function


[plus]

Rod's definitely a different approach, nice!

Tsh73 mine would look more like yours if I turn off the glitter effect:
global H$, XMAX, YMAX, nRing
H$ = "gr"
Xmax = 600 '<======================================== actual drawing space needed
Ymax = 600 '<======================================== actual drawing space needed

nomainwin

WindowWidth = Xmax + 8
WindowHeight = Ymax + 32
UpperLeftX = (DisplayWidth - Xmax) / 2  'or delete if XMAX is 1200 or above
UpperLeftY = (DisplayHeight - Ymax) / 2   'or delete if YMAX is 700 or above

open "Spinning Black Hole Attractor #3 = Ring O Stars" for graphics_nsb_nf as #gr
#gr "trapclose quit"
#gr "size 1"
#gr "down"
#gr "fill 60 0 30"

nstars = 60
Dim sx(nstars), sy(nstars), sr(nstars), sc$(nstars), tx(2000), ty(2000), tr(2000), tc$(2000)
cx = 300: cy = 300
'setup start stars
For i = 1 To nstars
   [tryagain]
   sx(i) = Rnd(0) * 600
   sy(i) = Rnd(0) * 600
   dx = cx - sx(i): dy = cy - sy(i)
   d = (dx * dx + dy * dy) ^ .5
   if d <= 52 then goto [tryagain]
   sr(i) = Rnd(0) * 3 + 1
   sc$(i) = rnd(0) * 128 + 128;" ";rnd(0) * 128 + 128;" ";rnd(0) * 128 + 128
Next
Do
   #gr "fill 10 0 30"
   'black Hole
   #gr "color 128 0 0"
   #gr "backcolor 0 0 0"
   #gr "place ";cx;" ";cy;"; circlefilled ";50
   'show stars
   for i = 1 to nRing ' on Ring  make glitter!
       'if rnd(0) < .3*nRing/nRing then 'glit
           dx = cx - tx(i): dy = cy - ty(i)
           b = Atan2(dy, dx)
           d = (dx * dx + dy * dy) ^ .5
           #gr "color ";tc$(i)
           #gr "backcolor ";tc$(i)
           #gr "place ";cx + d * cos(a + b);" ";cy + d * sin(a + b);"; circlefilled ";tr(i)
       'end if
   next
   For i = 1 To nstars
       dx = cx - sx(i): dy = cy - sy(i)
       b = Atan2(dy, dx)
       d = (dx * dx + dy * dy) ^ .5
       #gr "color ";sc$(i)
       #gr "backcolor ";sc$(i)
       #gr "place ";cx + d * cos(a + b);" ";cy + d * sin(a + b);"; circlefilled ";sr(i)
       'now update stars falling into black hole
       dx = cx - sx(i): dy = cy - sy(i)
       d = (dx * dx + dy * dy) ^ .5
       If d <= 53 Then 'black hole radius
           call newRing i
           call newStar i
       Else ' move it
           dx = 100 * dx / (d * d)
           dy = 100 * dy / (d * d)
           sx(i) = sx(i) + dx
           sy(i) = sy(i) + dy
       End If
   Next
   a = a + .006
   call pause 60
Loop until something

sub newRing i
   nRing = nRing + 1
   tx(nRing) = sx(i)
   ty(nRing) = sy(i)
   tr(nRing) = sr(i)
   tc$(nRing) = sc$(i)
end sub

Sub newStar i
   r = Int(Rnd(0) * 4) ' 0 to 3
   Select Case r
       Case 0
           sx(i) = Rnd(0) * 600
           sy(i) = 0
       Case 1
           sx(i) = Rnd(0) * 600
           sy(i) = 599
       Case 2
           sy(i) = Rnd(0) * 600
           sx(i) = 0
       Case 3
           sy(i) = Rnd(0) * 600
           sx(i) = 599
   End Select
End Sub

sub quit H$
   close #gr
   end
end sub

sub pause mil   'tsh version has scan built-in
   t0 = time$("ms")
   while time$("ms") < t0 + mil : scan : wend
end sub

Function Atan2(y, x)
   'Atan2 is a function which determines the angle between points
   'x1, y1 and x2, y2. The angle returned is in radians
   'The angle returned is always in the range of
   '-PI to PI radians (-180 to 180 degrees)
   '==============================================================
   'NOTE the position of Y and X arguments
   'This keeps Atan2 function same as other language versions
   '==============================================================
  If x = 0 Then
      If y < 0 Then
           Atan2 = -1.5707963267948967
       Else
           Atan2 = 1.5707963267948967
       End If
  Else
      chk = atn(y/x)
      If x < 0 Then
          If y < 0 Then
               chk = chk - 3.1415926535897932
           Else
               chk = chk + 3.1415926535897932
           End If
      End If
       Atan2 = chk
  End If
  'thanks Andy Amaya
End Function


Now you can see the stars build up around the ring.

b = b + ...

[honky]

In reality, after a few laps, the stars (and the rest) fall into the hole.
Simple history becomes more complex.

In my opinion, there are not enough stars and too many big stars
Maybe add fixed stars to relieve the processor (Those that are distant, Out of attraction, deep sky) .