Re:Commander Keen source code released
by Chinjut on Tuesday September 16, 2014 @09:45PM
(#8328062)
What's the relevance of these ratios to Carmack's purpose in extrapolating the series? At any rate, the limiting ratio of successive terms in the altered Fibonacci series 21,54,75,129,204,..., is the same as for the ordinary Fibonacci series, even if the convergence is slower (the difference between this altered Fibonacci series and the original Fibonacci series is just another version of the Fibonacci series, shifted over and multiplied by 20).
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Re:Commander Keen source code released
by sillysaurus3 on Tuesday September 16, 2014 @10:35PM
(#8328216)
Apparently Carmack didn't actually use it anyway, so I suppose there wasn't any purpose. But Carmack's series is significantly different from the normal Fibonacci series, because it only consists of the first ten elements, which isn't enough time to converge. If it was used in actual graphics or gameplay, it would have had a significantly different effect than a normal Fib sequence.
I just thought it was interesting, and another example of the same type of style which led to rocket jumping or bunnyhopping, which were also accidents.
Re:Commander Keen source code released
by Chinjut on Wednesday September 17, 2014 @01:21PM
(#8331125)
It's not clear that Carmack's purpose in using the Fibonacci series was to take successive ratios to approximate "the golden ratio" (if it was the golden ratio he cared about, he could just as well have directly calculated (1 + sqrt(5))/2). He quite possibly could have been interested in the Fibonacci sequence for some other reason, or no reason at all.