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Different loop expressions. #aftereffects Explanation for last 2 - loopOut("cycle") = loopOut() - i used cycle so we can add number 1 - (,1) means it loops only last 2 keyframes - you can increase number based on how many keyframes you have

92,088 просмотров • 3 лет назад •via X (Twitter)

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The Fibonacci sequence has a hidden rhythm. Take any number say, 7. Write out the Fibonacci numbers (0, 1, 1, 2, 3, 5, 8...) and look at the remainders when you divide by 7. You get: 0, 1, 1, 2, 3, 5, 1, 6... Keep going, and the pattern eventually repeats. The length of that repeating cycle is called the Pisano period. For most numbers, this cycle length is pretty unpredictable. But we proved something precise. If you ask "when does the cycle length equal exactly twice the number?" The answer is an infinite tower. 12, 60, 300, 1500, 7500...just keep multiplying by 5. But if you change the question slightly "when does the cycle length equal twice the square root?" there is exactly ONE answer. 144. Same skeleton. Two completely different outcomes. The culprit? The prime number 5 ,which has a weird superpower in Fibonacci land. it's the only prime that divides its own cycle length. In one equation it fits perfectly and builds an infinite tower. In the other, it overflows and gets kicked out leaving 144 all alone. Fun fact. 144 is also the only perfect square (besides 0 and 1) that appears anywhere in the entire Fibonacci sequence. Two totally different math questions from two totally different fields converging on the exact same number. The animation spins through the golden spiral, forges the 12-skeleton, ignites the self-supplying 5, then splits into two fates, 144 on the left, the infinite tower on the right. The Pisano Doubling Equations π(m) = 2m and π(m2 ) = 2m: One Skeleton, Two Fates The Prime Lattice Coherence Framework: A Unified Master Document

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36,480 просмотров • 18 дней назад