I am attached to the thread’s name. It strikes me as so outlandish that it deserves attention.
On the speculated history of song-birds was a recent paper suggesting most if not all songbirds appear to have had a singular ancestry from SE Asia or Australasia. If you seek to embellish the voice of sauropods with something more familiar to modern ears try cranes and herons. Melodic voices do seem to belong to Songbirds and not the aquatic residents. You guys are looking for fractals and stepping over more obvious solutions. Just prune the branches not the entire forest of mathematics. Any bird has only so much lung capacity so every utterance is limited to that volume and it must be forcibly discharged to create an audible wave. To be detectable by the intended target that sound must fall into a range of frequency and volume within the recipient’s capabilities. If the bird is unable to produce syrinx based sounds then it must devise an alternative like ruffed grouse or prairie chickens. They basically seem to beat the crap out of their chests and can sound like English motorcycles for brief moments. So let’s break away from some rather extreme avians from the Melodic Songsters of Poetry. Did not the Audubon Society have a library of Bird vocalizations, at one time. By the way Frisch did this sort of thinking with Honey Bee Waggle Dances and paper and pencil. As a student I had to read his work and found that the bees could sense extra dimensions which could include even more information, vibration and scent. Glad you are all back in a constructive mode. Suppose graphics of birdsongs could be transformed by functions from one species within a family to another to examine the environmental challenges that a species contends with say Mountain species compared to Plains species. Nick, I must bow to your wisdom and tip my hat. vib oh, Jon I saw you code site and will try and recompile/run it in Maple or Processing since I am familiar with those two. Some days are harder than others while pulling a barge upstream. Anyone recall any barge songs. vib From: Friam [mailto:friam-bounces @redfish.com] On Behalf Of Jon Zingale Sent: February-28-17 4:22 PM To: friam@redfish.com Subject: Re: [FRIAM] Fractal discussion Landscape-bird songs Nick, Well one way we may be able to understand birdsong as fractal might be by studying the underlying mechanism of the syrinx <https://en.wikipedia.org/wiki/Syrinx_(bird_anatomy)> . I can imagine this section of the birds trachea as a coupled oscillator, that when driven far from equilibrium could give way to trajectories along a strange attractor (which would be fractal). In an attempt to think about recovering the attractor from the time-series of the bird song, I ran across Takens' theorem last night. Then later last night (I couldn't sleep) I coded up an example of Takens' theorem in RubyProcessing <https://github.com/jonzingale/RubyProcessing/blob/600c83727c77a4d52ac4effe65d7258100bae5b4/lorenz/lorenz_reconstruction.rb> . What is amazing about this theorem is that it suggests how to build a low- dimensional manifold from a single dimensional time-series! So freaking cool. As a test case, I coded up the Lorenz equations and plotted the manifold. Then I calculated just the time series for the x dimension. Lastly, I reconstructed the entire manifold (topologically) from just this one coordinate! Included below is a screenshot of the visualizer. It is actually more fun to watch in motion, but the picture is telling in itself. Jon
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