DECLARE SUB epsylon ()
DECLARE SUB pseurnd ()
DECLARE SUB random1 ()
DECLARE SUB xpos ()
DECLARE SUB ypos ()
DECLARE SUB vuldicht ()
DECLARE SUB Titel ()
COMMON SHARED nx%, ny%, dd, eps%, nt%, nn
COMMON SHARED x%(), y%(), z%(), tel%()

RANDOMIZE TIMER
SCREEN 12
Titel

Nog:
CLS
COLOR 11
PRINT "    RANDOM fill of a space."
COLOR 15
PRINT : PRINT : PRINT
PRINT "      -> 1 = random distribution"
PRINT "      -> 2 = homogeneous distribution"
PRINT "      -> 3 = about RANDIST"
PRINT "      -> ENTER = Stop"
PRINT : PRINT : PRINT : COLOR 11
PLAY "l6b-"
INPUT "      -> Choice: ", kies$
IF kies$ = "" THEN
PLAY "l12c+egb->d"
END
END IF
IF kies$ <> "1" AND kies$ <> "2" AND kies$ <> "3" GOTO Nog

SELECT CASE kies$

CASE "1"
xpos
ypos
vuldicht
nn = nx% * ny% * dd
IF nn > 32000 THEN
nn = 32000: dd = nn / (nx% * ny%)
PRINT : COLOR 12
PRINT USING ">>> Overflow >>> taken maximum density ##.## "; dd
PLAY "o4l12d": SLEEP 2: COLOR 15
CLS
END IF
REDIM z%(nx% * ny%)
REDIM tel%(50)
WINDOW (0, 0)-(nx% + 1, ny% * 1.05)
CLS
COLOR 12
LOCATE 1, 30
PRINT USING "dens.= ##.##,  ##### = ### X ### positions"; dd; nx% * ny%; nx%; ny%
COLOR 15
random1
GOTO Nog

CASE "2"
 xpos
 ypos
 epsylon
 xx% = nx% / eps% + nx% MOD eps%     '''max. along x,
 yy% = ny% / eps% + ny% MOD eps%     '''             y,
 nt% = xx% * yy%                     '''expected max. occ.
 REDIM x%(nt%), y%(nt%)              '''occupied posns.
 CLS
 WINDOW (1, 1)-(nx% + 1, 1 + ny% * 1.05)
 pseurnd
 GOTO Nog

CASE "3"
 Titel
 GOTO Nog

END SELECT

END

SUB epsylon
eps:
PLAY "o4l12d": LOCATE 24, 1
INPUT " -> Choose min. distance (default=3, 1 thru Nx or Ny) : ", eps%
IF eps% = 0 THEN eps% = 3
IF eps% > nx% OR eps% > ny% OR eps% < 0 THEN
LOCATE 20, 1
PRINT "                                                                    "
PLAY "o4l12d"
GOTO eps
END IF
END SUB

SUB pseurnd
LOCATE 1, 1: COLOR 14:
PRINT USING "Posns. : ##### /Dist. : ## /Max.:##### /Fill: #####"; nx% * ny%; eps%; nt%; i%

 FOR i% = 1 TO nt%
worp2:
 x% = 1 + RND * (nx% - 1)
 y% = 1 + RND * (ny% - 1)
 IF i% = 1 THEN GOTO verder
 FOR j% = 1 TO i% - 1
 IF ABS(x% - x%(j%)) < eps% AND ABS(y% - y%(j%)) < eps% THEN
 tel1% = tel1% + 1
IF tel1% > 100 GOTO opvullen
 LOCATE 1, 60: COLOR 3: PRINT USING "Worp:###"; tel1%: COLOR 15
 GOTO worp2
 END IF
 NEXT j%

verder:
 tel% = tel% + 1
 x%(i%) = x%: y%(i%) = y%
 tel1% = 0

teken:
LOCATE 1, 47: COLOR 14: PRINT USING "#####"; i%: COLOR 15
LINE (x%, y%)-(x% + 1, y% + 1), , BF

volg:
IF INKEY$ <> "" THEN PRINT "STOP": END
NEXT i%

opvullen:                     '''look for holes, and fill
 tel1% = 0
 i% = i% - 1
 ii% = i%
 LOCATE 1, 60:  COLOR 3: PRINT "Filling... ": COLOR 15
PLAY "o4l12d"
FOR y% = 1 TO ny%
FOR x% = 1 TO nx%
 FOR j% = 1 TO i%
 IF ABS(x% - x%(j%)) < eps% AND ABS(y% - y%(j%)) < eps% GOTO volg2
 NEXT j%
i% = i% + 1
IF i% > nt% THEN i% = nt%: GOTO statist2
 x%(i%) = x%: y%(i%) = y%
 tel1% = tel1% + 1

teken2:
PLAY "o4l12d"
LOCATE 1, 47: COLOR 14: PRINT USING "#####"; i%: COLOR 15
LOCATE 1, 60:  COLOR 3: PRINT USING "Filling : ####"; tel1%: COLOR 15
LINE (x%, y%)-(x% + 1, y% + 1), 3, BF

volg2:
 NEXT x%
 NEXT y%

statist2:
LOCATE 1, 60: COLOR 11: PRINT "-> Key...       "
PLAY "o2l6a>l12fedc+"
SLEEP: a$ = INKEY$
CLS
PRINT USING "Fill stats. about the ##### occupations:"; i%
PRINT : PRINT : COLOR 15
PRINT "             number of positions : "; nx% * ny%
PRINT "               required distance : "; eps%
PRINT "                  max. occupancy : "; nt%
PRINT "   occupancy achieved by tossing : "; ii%
PRINT "                   by filling in : "; i% - ii%
PRINT "        total occupancy achieved : "; i%
PRINT "             equivalent distance : "; : PRINT USING "###.#"; SQR(nx% * ny% / ii%)
PRINT : PRINT : PRINT
COLOR 11: PRINT " -> Key...  "
COLOR 15
PLAY "l6d<a"
SLEEP: a$ = INKEY$

END SUB

SUB random1
FOR i% = 0 TO nn
testx% = INT(RND * nx%): testy% = INT(RND * ny%)
COLOR 14: LOCATE 1, 1: PRINT i%: COLOR 15
LINE (testx%, testy%)-(testx% + 1, testy% + 1), , BF
test% = testy% * nx% + testx%
z%(test%) = z%(test%) + 1
NEXT i%

FOR i% = 0 TO nx% * ny%
tel%(z%(i%)) = tel%(z%(i%)) + 1
NEXT i%

COLOR 11: LOCATE 1, 15: PRINT "-> Key...  ": COLOR 15
PLAY "o2l6a>l12fedc+"
SLEEP: a$ = INKEY$
CLS : COLOR 11
PRINT USING "Fill stats. about the ##### positions (##### tosses)"; nx% * ny%; nx% * ny% * dd
PRINT : PRINT : COLOR 15
FOR i% = 0 TO 20
PRINT USING "##.# %  #####  times selected"; tel%(i%) / (.01 * nx% * ny%); i%
NEXT i%
PRINT : PRINT : PRINT
COLOR 11: PRINT " -> Key...  "
COLOR 15
PLAY "l6d<a"
SLEEP: a$ = INKEY$
END SUB

SUB Titel
CLS
COLOR 11
PRINT "    RANDOM fill of a space.                    (1/3) -> Key...  "
COLOR 15
PRINT : PRINT : PRINT
PRINT "Is a random distribution of matter in space homogeneous?"
PRINT "Is a homogeneous distribution random?"
PRINT
PRINT "In this program the two notions are being displayed, both applying"
PRINT "for the label 'random'."
PRINT "Space in our case consists of a field of (x,y) positions,"
PRINT "number to be chosen. Each toss (x,y) is itself fully random."
PRINT
PRINT "Our first kind of distribution accepts each toss. As a consquence,"
PRINT "positions may be occupied more than once (something matter couldn't do)."
PRINT "Other positions may stay vacant. The end result depends largely on "
PRINT "the ratio between the numbers of tosses and of available positions."
PRINT
PRINT "The second distribution accepts only tosses that maintain a given"
PRINT "minimal distance to positions already occupied. No double occupation"
PRINT "in this case: it's like a swarm of bats keeping distance amongst"
PRINT "each other."
PRINT
PRINT "What kind of distribution you think corresponds best to matter in space?"
PRINT "So what about the search for structure in the universe, what with clusters,"
PRINT "superclusters and bubbles: shouldn't we relativize a bit there?"
LOCATE 28, 1: COLOR 10: PRINT "    Credits: Guido Wuyts 1996"
PLAY "o2l6a>l12fedc+"
COLOR 11
SLEEP: a$ = INKEY$
CLS
COLOR 11
PRINT "    RANDOM fill of a space.                    (2/3) -> Key...  "
COLOR 15: PRINT : PRINT : PRINT
PRINT "    1. Random distribution."
PRINT
PRINT "Consider a space of N = Nx.Ny positions, arranged along"
PRINT "x- and y-directions of Nx and Ny places respectively."
PRINT "Fill positions in this space through randomly tossing (x,y)."
PRINT "Each toss at equal chance."
PRINT
PRINT "Do N times D tosses: D = fill density (ratio tosses/positions)."
PRINT "Check following questions:"
PRINT
PRINT " -> % of positions selected 1, 2, 3... times?"
PRINT " -> % of positions remaining empty?"
PRINT " -> starting from which density D fill almost complete?"
PRINT
PRINT " Notice also, for smaller densities, pseudostructures in the shape of"
PRINT " clusters, for larger ones in the shape of holes (bubbles): random"
PRINT " distribution is Not homogeneous! By the way, this is a fractal "
PRINT " property that holds for all scales of material fill: "
PRINT " nebulae, galaxies, clusters and beyond..."
LOCATE 28, 1: COLOR 10: PRINT "    Credits: Guido Wuyts 1996"
PLAY "l6d"
SLEEP: a$ = INKEY$
CLS
COLOR 11
PRINT "    RANDOM fill of a space.                    (3/3) -> Key...  "
COLOR 15: PRINT : PRINT : PRINT
PRINT "    2. Homogeneous distribution."
PRINT
PRINT "The same space with Nx.Ny = N positions. All tosses (x,y) equally"
PRINT "random. This time, we fill only (x,y) if distance to all previous"
PRINT "occupations exceeds a chosen minimum."
PRINT "Otherwise the toss is ignored and a next toss made."
PRINT
PRINT "Once the number of successive 'vain' tosses exceeds a hundred,"
PRINT "density of occupation has reached a point where chances at a new"
PRINT "toss that proves 'right' decrease rapidly. For practical purposes we"
PRINT "then change strategy. We scan sequentially all positions and check"
PRINT "them for 'fillability'. Thus we reach the maximum fill that is -yet-"
PRINT "possible after the random toss stage."
PRINT
PRINT "Chances are it isn't the maximum possible fill, given the minimal"
PRINT "distance: that would be a regular crystal grid fill. Our "
PRINT "homogeneous distribution then holds an element of randomness."
PRINT "Some statistics compare the distances required and obtained, "
PRINT "and corresponding numbers of occupation."
LOCATE 28, 1: COLOR 10: PRINT "    Credits: Guido Wuyts 1996"
PLAY "<l6a"
SLEEP: a$ = INKEY$


END SUB

SUB vuldicht
vul:
PLAY "o4l12d": LOCATE 24, 1
INPUT " -> Choose fill density (default=.25, 0+ thru 10) : ", dd
IF dd = 0 THEN dd = .25
IF dd < 0 OR dd > 10 THEN
LOCATE 24, 1
PRINT "                                                                    "
PLAY "o4l12d"
GOTO vul
END IF
END SUB

SUB xpos
xpos:
PLAY "o4l12d": LOCATE 20, 1
INPUT " -> Choose nr. of x-positions (default=65, 10 thru 200) : ", nx%
IF nx% = 0 THEN nx% = 65
IF nx% < 10 OR nx% > 200 THEN
LOCATE 20, 1
PRINT "                                                                    "
PLAY "o4l12d"
GOTO xpos
END IF
END SUB

SUB ypos
ypos:
PLAY "o4l12d": LOCATE 22, 1
INPUT " -> Choose nr. of y-positions (default=40, 5 thru 150) : ", ny%
IF ny% = 0 THEN ny% = 40
IF ny% < 5 OR ny% > 150 THEN
LOCATE 22, 1
PRINT "                                                                    "
PLAY "o4l12d"
GOTO ypos
END IF
END SUB