Quite BASIC — Fibonacci Squares

BASIC Program

1000 REM Fibonacci Squares Project
1010 REM Quite BASIC Math Project
1020 REM ------------------------ 
2010 CLS
2020 REM (X, Y) are corner coordinates for squares
2030 REM The corners are between pixes -- that explains the 0.5 business
2030 LET X = 31.5
2040 LET Y = 31.5
2050 REM C is an array of five color names
2060 ARRAY C
2070 LET C[0] = "cyan"
2080 LET C[1] = "green"
2090 LET C[2] = "red"
2100 LET C[3] = "blue"
2110 LET C[4] = "yellow"
2060 REM The array F holds the Fibonacci numbers
2070 ARRAY F
2070 LET F[0] = 0
2080 LET F[1] = 1
2090 LET N = 1
2100 REM The main loop starts here
2110 GOSUB 3000
2120 REM Here we compute the next Fibbonacci number
2120 LET F[N+1] = F[N] + F[N-1]
2130 LET N = N + 1
2140 REM Stop after printing 8 squares
2150 IF N <= 8 THEN GOTO 2100
2160 END
3000 REM ------------------------
3010 REM Subroutine -- Draw a tile
3020 PRINT F[N]
3030 REM (P, Q) is the diagonal of the tile
3040 REM We use trigonometry to set the diagonal's direction
3050 LET A = PI * (N / 2 - 1/4)
3060 LET P = ROUND(SQR(2) * SIN(A))
3070 LET Q = ROUND(SQR(2) * COS(A))
3080 REM Loop over the pixels of the tile in two dimensions 
3090 FOR I = X+P*0.5 TO X+P*(F[N]-0.5) STEP P
3100 FOR J = Y+Q*0.5 TO Y+Q*(F[N]-0.5) STEP Q
3110 REM Note: % is the modulo operator
3120 REM we use it here to make sure the index of C stays between 0 and 4
3130 PLOT I, J, C[N%5]
3140 NEXT J
3150 NEXT I
3160 REM Update X and Y before returning
3170 LET X = X + P * F[N]
3180 LET Y =Y + Q * F[N]
3190 RETURN

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