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Active Forums => Programs => Topic started by: STxAxTIC on December 15, 2020, 06:12:18 am

Title: MYOFS
Post by: STxAxTIC on December 15, 2020, 06:12:18 am
This is a bite-size piece of code that's been lingering on my desktop for a while and it needs a new home.

MYOFS stands for "Make your own Fibonacci sequence". It turns out that that usual 1 1 2 3 5 8 13... thing can be generalized. A little backstory first. The Fibonacci sequence, as we all know it, can actually be generated by doing something cute with the golden ratio. That is, a number close to 1.618 seeds the entire sequence. This program lets you change the seed parameter from the golden ratio to whatever you want, generating the appropriate sequence.

Once that gets boring, the game becomes finding new sequences that are all integers, not just a bunch of decimals. Welp, turns out there are many of these cases. Un-comment some other initial x-values to get them:

Code: QB64: [Select]
  2.  
  4. DIM Coefficient(21) AS DOUBLE
  6. x = 1 / 2 + SQR(5) / 2
  7. 'x = 1 + SQR(2)
  8. 'x = 3 / 2 + SQR(13) / 2
  9. 'x = 2 + SQR(5)
  11.     CLS
  12.     IF (_KEYDOWN(18432) = -1) THEN ' Up-arrow
  13.         x = x + .01
  14.     END IF
  15.     IF (_KEYDOWN(20480) = -1) THEN ' Down-arrow
  16.         x = x - .01
  17.     END IF
  18.     _KEYCLEAR
  19.     Coefficient(1) = 1
  20.     Coefficient(2) = x - 1 / x
  21.     PRINT "x="; x
  22.     PRINT "C_1="; Coefficient(1)
  23.     PRINT "C_2="; Coefficient(2)
  24.     FOR k = 3 TO UBOUND(Coefficient)
  25.         Coefficient(k) = -1 * Coefficient(k - 2) + x ^ (k - 1) + (-1) ^ (k - 1) * 1 / (x ^ (k - 1))
  26.         PRINT "C_"; LTRIM$(RTRIM$(STR$(k))); "="; Coefficient(k) ', Coefficient(k) / Coefficient(k - 1)
  27.     NEXT
  28.     _LIMIT 60
  29.     _DISPLAY
  31.  
Title: Re: MYOFS
Post by: bplus on December 15, 2020, 10:34:59 am
I suspect Pythagorean Triples are in play for all integer sequences, I will check this out after I figure out how to defeat a certain pattern of moves against AI, ha, ha!

@STxAxTIC what's your favorite charity?
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