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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.math Subject: Re: Rotation Bifurcation... Date: Sat, 30 Mar 2024 13:24:35 -0700 Organization: A noiseless patient Spider Lines: 44 Message-ID: <uu9se4$16otk$2@dont-email.me> References: <uu7m3v$jh52$1@dont-email.me> <uu9dvq$13amk$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sat, 30 Mar 2024 20:24:36 +0100 (CET) Injection-Info: dont-email.me; posting-host="e3ffe136872d6b59fa10d485f79c0803"; logging-data="1270708"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+U356ICo5FKArL90n3440xcRD0nv++WaQ=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:bEWOftYJA6JIq5x+jgV/5js5vKA= Content-Language: en-US In-Reply-To: <uu9dvq$13amk$2@dont-email.me> Bytes: 2510 On 3/30/2024 9:18 AM, Volney wrote: > On 3/29/2024 8:24 PM, Chris M. Thomasson wrote: >> A strange bifurcation algorithm from an older iterated function system >> of mine: >> >> https://youtu.be/XKhS_nklCkE >> >> My pseudo code is in the description: >> >> ______________ >> // px_mutation interpolates from -4...4 across each frame; 1440 here. >> >> render frames: >> _________ >> // angle interpolates from 0...pi2 across iterations >> // px = py = 0 >> >> // Iteration: >> px = sin(angle * px_mutation); >> py = cos(angle * py); >> ______________ >> >> Anybody should be able to reproduce it on their end. Right? >> >> It's all 2d, but has a 3d vibe! Nice. >> >> Any thoughts? > > It looks like a fractal version of an optical illusion of whether a > cylinder (with the fractal on it) is rotating in one direction or the > other. Notice the alpha blend where we can see through the illusion of a 2d plane looking 3d even with a completely 2d IFS? I did some simple 3d volumetric protrusions of it. Well, it looks like some sort of strange helix curve. px_mutation going from -4...4 across the frames (1440) here is the main animation driver, so to speak. when px_mutation hits zero, the plane is on edge where we can see a thin vertical line. In the volumetric we can see how its a plane because we can move the camera around it. You can see this moment right around this time: https://youtu.be/XKhS_nklCkE?t=29