Golden yucca

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    This is a Fibonacci spiral; the linear size of each square is a Fibonacci number. Let F_{n} denote the n'th Fibonacci number. Then it is clear from this figure that F_{n} = F_{n-1} + F_{n-2}; the length of each side is the sum of the lengths of the previous two sides. It is also clear the areas of all the squares add up the the area of the large rectangle; that is: (F_1)^2 + (F_2)^2 + ... + (F_n)^2 = F_{n}*F_{n-1}.

    You can read more about the Fibonacci spiral, and it's cousin the Golden spiral, on wikipedia.

    You won't be surprised that I also wrote a Gimp script to make these things automatically. You would be surprised (or appalled) to know how long it took me to finally debug it...

    Now available at the Gimp registry.

    ℙαґḯṧḯ℮ηηε and Andres DC added this photo to their favorites.

    1. gracieshoots 64 months ago | reply

      This is fun, and I would be surprised if it took less than a month to debug it, and I was thinking about golden shapes today. How coincidental.

    2. stay-at-home-gypsy 64 months ago | reply

      Is it for sale on yet???

    3. theilr 64 months ago | reply

      Thanks, I actually posted one of these awhile back (see below) which, now that I remember to look at it, I prefer to this one. But that one was done by hand, this one by script. The original script wasn't that hard, but this one works on portrait and landscape mode, and lets you put the spiral center in any of the four quadrants. Getting the bookkeeping straight so that all those eight cases would work correctly was where all the debugging came in.

      well, not on Amazon...yet. But I just uploaded it to the Gimp registry.

      railroad track spiral

    4. fuzzy jr 64 months ago | reply

      im sitting here looking at this, and reading your explanation ... and just find myself looking and looking and ....

      i've seen some others that try this, but yours is really well done and the explanation in your comments actually makes sense. thank you...

      i love how you take something simple and make it so intriguing!

    5. theilr 64 months ago | reply

      thanks! i'm really pleased that the explanation makes sense. as for the looking and looking, i think that's the animation, it's (designed to be) a little hypnotic...

    6. ℙαґḯṧḯ℮ηηε 64 months ago | reply

      I really need to learn to use Gimp because I really want to do this!!!

    7. Prof. Tournesol 64 months ago | reply

      Very cool. You really have quite an imagination!

      Happy New year!

    8. theilr 64 months ago | reply

      thanks! there are lots of reasons to use the Gimp (not least of which is that it's free), but i'm sure you could do this with Photoshop just as well, except it's a little tedious without a script.
      thanks, i take that as high praise...happy new year to you too!

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