Anishchenko Astakhov Attractor
thingiverse
<head>Jean-Marc Daviau-Williams<br />George Mason University<br />MTH401 Math Through 3D Printing</head> <body><p>This week's print focused on chaotic attractors, a result of specific non-linear differential equations that, when graphed, exhibit non-periodic behavior and fail to converge inward, making them difficult to predict. This phenomenon earned the name [<a target="_blank" href="http://www.stsci.edu/~lbradley/seminar/attractors.html">1</a>] due to its unpredictable nature.</p><p>The attractor in question was discovered by Vadim Anishchenko, a Russian mathematician who extensively researched this subject. His work is notable, particularly in relation to the Lorenz attractor [<a target="_blank" href="http://downloads.hindawi.com/journals/ddns/1998/252749.pdf">2</a>].</p><p>To create this print, I built upon the provided Mathematica code, adjusting values and definitions as necessary to achieve the desired shape. This process involved significant trial and error, but ultimately yielded a sea shell-like shape that pleased me.</p><p>The printing phase was straightforward, utilizing the Makerbot in the GMU Math Makerlab. I selected neon green filament for its captivating color. However, upon completion, the print required extensive sanding to remove the support raft, resulting in a beautiful finish but a small size that failed to demonstrate the attractor's behavior.</p><p>Undeterred, I decided to reprint the object with an increased scale and longer run time, which resulted in a coiled snake shape. This design change allowed for easier observation of the discrete tubes and attractor sequence. The second print was four times larger than its predecessor and featured black filament, offering improved visibility despite a less aesthetically pleasing appearance.</p><p>Sources:<br />1) <a target="_blank" href="http://www.stsci.edu/~lbradley/seminar/attractors.html">Bradley</a>. (n.d.). Retrieved from http://www.stsci.edu/~lbradley/seminar/attractors.html.<br />2) Anishchenko, V. S., & Strelkova, G. I. (1998). Irregular Attractors. Discrete Dynamics in Nature and Society, 2(1), 53–72. doi: 10.1155/s1026022698000041</p></body>
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