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Fractal Koch curve math in GWBASIC, BASICA

Calculates the increasing area within the Koch snowflake as the number of segments is increased.

It shows that the fractal dimension of the curve is the limit that the area approaches but can never reach because it requires an infinite number of iterations to get there.

KOCHMATH.BAS

10 'KOCHMATH.BAS 7/28/88 
11 'COPYRIGHT (C)1988 STEVEN WHITNEY.
12 'Published under GNU GPL (General Public License) Version 3, with ABSOLUTELY NO WARRANTY.
13 'Initially published by http://25yearsofprogramming.com.
20 'CALCULATES THE MATH ASSOCIATED WITH THE KOCH CURVE.
30 'ALL IT REALLY DOES IT PRINT SOME LINES OF NUMBERS, BUT
35 'THOSE NUMBERS SHOW THAT...
40 'THE FRACTIONAL DIMENSION OF THE KOCH CURVE IS THE 
45 'LIMIT TOWARDS WHICH THE INCREASED AREA GOES!
80 DEFDBL A,L,S,C
90 LENGTH=3
100 AREA= SQR(3)/4
110 LASTAREA=AREA
120 PRINT "I","AREA","CUM.DIFF."
130 FOR I=1 TO 42
140 	SEGS = (3 * 4^I) - (3 * 4^(I-1))
150 	SEGAREA = (SQR(3)/4) * 1/(9^I)
160 	LENGTH=LENGTH * 4/3
170 	AREA = AREA + SEGS/3 * SEGAREA
180 	CUMAREA=CUMAREA+(AREA-LASTAREA)
190 	PRINT I,AREA,CUMAREA
200 	LASTAREA=AREA
210 NEXT I