**Julia Fractals (type Byers)**

**
QBASIC and QuickBASIC compatible code (see below) to generate fractals similar to picture.
A 486 computer or 386 with math processor is highly
recommended since the SQR (square-root function) takes considerable time otherwise.
The program also demonstrates how to get 64*64*64 = 262144 (256K) different colors
assuming you have 256K video memory and a VGA color monitor (IBM-compatible computers).
Also, only 16 different colors of any of the 256K colors can be shown
in any picture. The PALETTE command can change the color of any of the 16 possible
in the picture. Combinatorial mathematics can solve how many different combinations of 16
colors can be chosen from among the 262144 colors. The formula is 262144!/(16!*(262144-16)!) where ! stands for factorial.
The fantastic number is 4.97*10^86/2.092*10^13 = 2.376*10^73 combinations. I use the ^ to mean
to the power of. If one looked at all possible combinations each one for just a millisecond, then it would take trillions and trillions of times longer than
the universe is old (15 billion years). Another comparison is that if there are 1 million grains of
very fine sand in a cubic centimeter then there are 10^33 grains of this sand in the earth
and if there are a trillion earths in a galaxy and a trillion galaxies in the universe then there is
still only 10^57 grains of sand in the universe (much less than the number of possible color combinations)!
**

10 CLS : A = RND(-TIMER): SCREEN 12: DEFINT K: XS = 640: YS = 480

20 IT = XS / 2: JT = YS / 2: S = 3 / YS: T = 3 / XS

30 P = RND * .15 + .38: Q = RND * .15 + .04

40 FOR YY = -1.6 TO 1.6 STEP S: FOR XX = -1.4 TO 1.4 STEP T

50 X = XX: Y = YY: K = 0: I = XS / 3 * XX + IT: J = YS / 3 * YY + JT

60 A = X * X - SQR(ABS(Y)) * SQR(ABS(Y)) * P: IF A$ = CHR$(27) THEN END

70 B = 2 * SQR(ABS(X)) * SQR(ABS(Y)) + Q: X = A: Y = B: K = K + 1

80 M = X * X + Y * Y: IF K > 32 THEN 100

90 IF M < 4 THEN 60 ELSE GOSUB 130

100 NEXT: A$ = INKEY$: NEXT

110 A$ = INKEY$: IF A$ = "" THEN GOSUB 120: GOTO 110 ELSE 30

120 K = INT(RND * 15)

130 I = XS / 3 * XX + IT: J = YS / 3 * YY + JT: PSET (I, J), K MOD 15

140 IF RND < .001 THEN

150 BLUE% = INT(RND * 63) + 1: GREEN% = INT(RND * 63) + 1

160 RED% = INT(RND * 63) + 1: CN& = 65536! * BLUE% + 256 * GREEN% + RED%

170 PA% = INT(RND * 15) + 1: PALETTE PA%, CN&

180 END IF: RETURN

(C) 1995 by John A. Byers