rem Julia Sets ...... Rev 5.2
      rem A J Tooth / 1st February 2003 Revised 28th June 2003
      
      rem Set up use of Full Screen
      proc_fullscreen(22)
      xlim%=2048 : ylim%=1536
      dim Col%(7,6)
      a$=inkey$(10)
      rem Parameter Setup
      print " Either enter your own parameters, or choose a point on the MANDELBROT set."
      print " Press -m- for the Mandelbrot option, or spacebar to enter your own."
      
      rem Sets up eight levels of random colour
      proc_eight
      
      a$=get$ : cls
      if a$="m" then
        rem Preset parameters
        lmt%=127 : rl=-2 : ru=2 : il=-2 : iu=2 : cm%=1000000
        rem Initial Mandelbrot picture
        proc_mandinit
      else
        cls : print " Enter personally chosen parameters. " : print
        input " Iteration limit (65)",lmt%
        input " Lower real limit (-2)",rl
        input " Upper real limit (2)",ru
        input " Lower imag. limit (-2)",il
        input " Upper imag. limit (2)",iu
        input " Julia Parameter value 1 (0.45)",cr
        input " Julia Parameter value 2 (0.7)",ci
        input " Complex Modulus limit (1,000,000)",cm%
      endif
      cls : clg
      
      rem Colour scheme options
      repeat
        input " Leave colours as random, or choose a range. Enter -d- or -r-. ",ch$
      until (ch$="d" or ch$="r")
      c$=ch$
      if c$="r" then
        proc_colran
      else
        rem Random colours already set above
      endif
      
      rem Repeats from here after PROC_zoom
  470 cls : clg
      repeat
        input " Enter q for quick and s for slow output ",spd$
      until (spd$="q" or spd$="s")
      cls : clg
      
      rem MAIN: Iteration Section
      if spd$="q" then st%=8 else st%=2
      
      for a%= 0 to xlim% step st%
        for b%= 0 to ylim% step st%
          rem Set initial values
          proc_init(cr,ci)
          stp%=1 : Et%=0
          rem Main Procedure for Julia/Mandelbrot calculations
          proc_julman(cr,ci)
          rem Go and get the colours
          proc_cols
          rem Plots a SINGLE PIXEL
          move a%,b% : draw a%,b%
        next b%
      next a%
      
      rem End of Main Body
      rem Primary Exit & Repeat Options
      sp$=get$
      if sp$="s" then goto 790
      if sp$="m" then
        proc_zoom
      else run
      endif
      goto 470
  790 quit
      end
      rem End of Programme ---------------------------------------
      :
      rem PROC 1
      rem Sets Colour Range
      def proc_colran
      input " Select base colour. Enter r,g or b. ",bs$
      input " Select low(1), medium(2) or high(3) or max(4) intensity. Enter 1,2,3 or 4. ",in%
      print " Using the same colour for base and range is OK."
      input " Enter ranging colour (r,g or b). ",rn$
      input" Enter third colour (r,g or b) if required or enter (x) if not required. ",ot$
      input " Use 64 colour gradations in Slow mode or only 16. Enter -h- or -l-. ",gr$
      case gr$ of
        when "h" : gr%=64
        when "l" : gr%=16
      endcase
      case bs$ of
        when "r" : Red%=63*in% : Green%=0      : Blue%=0
        when "g" : Red%=0      : Green%=63*in% : Blue%=0
        when "b" : Red%=0      : Green%=0      : Blue%=63*in%
      endcase
      endproc
      :
      rem PROC 2
      rem Set initial values
      def proc_init(Cr,Ci)
      local x,y
      x=rl+(a%/xlim%)*(ru-rl)
      y=il+(b%/ylim%)*(iu-il)
      r=x*x-y*y-Cr : i=2*x*y-Ci
      zmod=sqr(r*r+i*i)
      endproc
      :
      rem PROC 3
      rem Set up use of Full Screen
      def proc_fullscreen(N%)
      sys "GetSystemMetrics", 0 to xscreen%
      sys "GetSystemMetrics", 1 to yscreen%
      sys "SetWindowLong",@hwnd%,-16,&16000000
      sys "SetWindowPos",@hwnd%,-1,0,0,xscreen%,yscreen%,0
      mode N%
      mouse off : off : rem Turns off the Mouse Pointer and the Cursor
      endproc
      :
      rem PROC 4
      rem Enables user to zoom into a particular area
      def proc_zoom
      local x%,y%,b%,ax%,bx%,ay%,by%,rnl,inl
      mouse on : gcol 7
      rem Select first corner of rectangular zoom area
      repeat
        mouse x%,y%,b%
        ax%=x% : ay%=y%
      until b%=4
      rem Print a "+" at the first corner
      move ax%-10,ay% : draw ax%+10,ay%
      move ax%,ay%-10 : draw ax%,ay%+10
      rem Select opposite corner of zoom area
      repeat
        mouse x%,y%,b%
        bx%=x% : by%=y%
      until b%=1
      rem Draw a box and wait 1 second before moving on
      move ax%,ay% : draw bx%,ay% : draw bx%,by%
      draw ax%,by% : draw ax%,ay%
      a$=inkey$(100)
      
      rem Re-assign corner points in ascending order
      if ax%<bx% then
        lx%=ax% : ux%=bx%
      else
        lx%=bx% : ux%=ax%
      endif
      if ay%<by% then
        ly%=ay% : uy%=by%
      else
        ly%=by% : uy%=ay%
      endif
      rem Re-assign viewing window limits
      rnl=rl+((ru-rl)*(lx%/xlim%))
      rnu=rl+((ru-rl)*(ux%/xlim%))
      
      inl=il+((iu-il)*(ly%/ylim%))
      inu=il+((iu-il)*(uy%/ylim%))
      rl=rnl : il=inl
      ru=rnu : iu=inu
      mouse off
      endproc
      :
      rem PROC 5
      rem Calculates colour to use, depending on how fast function exceeds limit
      def proc_cols
      case c$ of
        when "d" :  rem Uses random palette
          Ntn%=16*(stp% mod 16) : lev%=stp% div 16
          if lev%>10 then lev%=10
          fct=Ntn%/256
          Red%=  int(fct*Col%(lev%,1)+(1-fct)*Col%(lev%,4))
          Green%=int(fct*Col%(lev%,2)+(1-fct)*Col%(lev%,5))
          Blue%= int(fct*Col%(lev%,3)+(1-fct)*Col%(lev%,6))
          
        when "r" : rem Uses custom colours
          rem Always only uses 16 colours in Quick mode (64 not easy to see!)
          Ntn%=(256/gr%)*(stp% mod gr%)
          lev%=stp% div gr% : if lev%>4 then lev%=4
          rem Colours alternate between increasing and decreasing in intensity
          if (lev% mod 2)=1 then Ntn%=gr%-Ntn%
          case rn$ of
            when "r" : Red%=Ntn%
            when "g" : Green%=Ntn%
            when "b" : Blue%=Ntn%
          endcase
          case ot$ of
            when "r" : Red%=63*lev%
            when "g" : Green%=63*lev%
            when "b" : Blue%=63*lev%
            otherwise
              rem Do nothing
          endcase
      endcase
      
      rem Set colour to Black if Zmod remains finite
      if stp%=lmt% then f%=0 else f%=1
      rem Continually reassigns Colour 10 to be the new hue
      vdu 19,10,16,(f%*Red%),(f%*Green%),(f%*Blue%)
      gcol 0,10
      endproc
      :
      rem PROC 6
      rem Main Julia / Mandelbrot Routine
      def proc_julman(Cr,Ci)
      local rnex, inex
      repeat
        rem Iterates calculation of Fn(Z)=Z*Z-c
        rem Then checks how big Fn(Z) is, until it exceeds some limit
        stp%=stp% + 1
        rnex=r*r-i*i-Cr : inex=2*r*i-Ci
        r=rnex : i=inex
        zmod=sqr(r*r+i*i)
        
        rem Press spacebar to "crash" out the programme and start again
        if inkey(-99) then quit
        rem Set loop exit criteria
        if zmod>cm% then Et%=1
        if stp%=lmt% then Et%=1
      until Et%=1
      endproc
      :
      rem PROC 7
      rem Draws initial Mandelbrot Set to select Julia parameters from
      def proc_mandinit
      local x,y,p%,q%
      for p%= 0 to xlim% step 4
        for q%= 0 to ylim%/2 step 4
          rem Set initial values
          x=rl+(p%/xlim%)*(ru-rl)
          y=il+(q%/ylim%)*(iu-il)
          r=x*x-y*y-x : i=2*x*y-y
          zmod=sqr(r*r+i*i)
          crt=x : cit=y
          stp%=1 : Et%=0
          rem Calculate Mandelbrot Set
          proc_julman(crt,cit)
          rem Go and get the colours
          proc_cols
          rem Plots a SINGLE PIXEL
          move p%,q% : draw p%,q%
          move p%,1536-q% : draw p%,1536-q%
        next q%
      next p%
      
      rem Enables selection of Julia parameter using the mouse.
      mouse on 3 : gcol 7
      repeat
        mouse real%,imag%,m%
        X=rl+(real%/xlim%)*(ru-rl)
        Y=il+(imag%/ylim%)*(iu-il)
        print tab(5,2);"Click on the left mouse button at an interesting point."
        print tab(5,5);"Present Point is; ";X;",";Y;"      ";
      until m%=4
      cr=X : ci=Y
      print tab(5,7);"Julia Parameters selected."
      b$=inkey$(100)
      mouse off
      endproc
      :
      rem PROC 8
      rem Sets up eight levels of random colours
      def proc_eight
      for s%=0 to 7
        c$="d" : cs%=rnd(3)
        rem Singles out one of the primary colours as prevalent
        Rinit%=-63*(cs%=1)+rnd(191)
        Ginit%=-63*(cs%=2)+rnd(191)
        Binit%=-63*(cs%=3)+rnd(191)
        Col%(s%,1)=Rinit% : Col%(s%,2)=Ginit% : Col%(s%,3)=Binit%
        Col%(s%,4)=int(Ginit%/2)
        Col%(s%,5)=int(Binit%/2)
        Col%(s%,6)=int(Rinit%/2)
      next s%
      endproc