Mon, Sep 23, 4:21 AM CDT

Spherical Helix

Other Apps Fractal posted on Mar 22, 2012
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Description


This is just a quicky from last weekend (something RENDERED before I go on posting photos). The idea behind it is an logarithmic helix that extends into all three dimensions, quite the same as I did to the binary tree. The radius both of the curve and grows the spheres by 2% with every step of 10°. Doing a complete loop, the growth factor is 2.03. I did 12 loops, yielding to a scale factor of well over 10000 (from the smallest ball of the first to biggest of the last loop). This way, both ends of the figure are invisible, either outside the frame or within a single pixel. Funnily, as both horizontal and vertical angle rotate with the same speed, both change the sign at the same time. Therefore, x never reaches negative values, as the square of the cosine is always above zero. Actually, the body looks differend from each direction. Using the spheres like a chain of pearls turned out much easier that trying to generate a continuous tube. Furthermore, I believe ist looks better. R=R_0*1.02^(phi/36°) x=R*cos^2(phi) y=R*sin(phi)*cos(phi) z=R*sin(phi) Grapher 2.03 (basic calculations) AutoCAD 2002 (drawn and rendered) Corel Photopaint 7 WordPad (MS-Office 2000)

Comments (1)


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Fidelity2

8:58AM | Fri, 23 March 2012

It is very cool. I thank you for this one. You are very talented. 5+!


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