Title: Fit Earth into a Globus on Your Desk - C1 fractal Sphere Post by: kram1032 on August 25, 2017, 08:04:47 AM Perhaps you remember the C1-fractal torus that was a flat torus (by its curvature) in 3D space?
(http://hevea-project.fr/imgPageTore/image_tore_PNAS_reduite.png) Well, the same people now have done a similar transformation to a sphere to shrink it to arbitrarily small sizes. (http://hevea-project.fr/imgPageSphere/interieur_sphere_reduite_055.jpg)(http://hevea-project.fr/imgPageSphere/file_0066.png) Check out the explanation here: http://hevea-project.fr/ENPageSphereDossierDePresse.html I believe this might also be related to what's going on here: [Iterative Sinus-Curve and the extension of line-curves] (https://www.fractalforums.com/index.php?topic=25531.msg101396#msg101396) (https://www.fractalforums.com/index.php?action=dlattach;topic=25531.0;attach=14487) but I'm not sure. Title: Re: Fit Earth into a Globus on Your Desk - C1 fractal Sphere Post by: Tglad on August 26, 2017, 01:36:11 PM I like the visuals. Unlike the sinus link, these are not fractals, they don't have infinite surface area, they have well defined normals, and the dimension of the surface is 2. If you keep zooming they get smoother and flatter. However, you might say that their derivative is a fractal. If a fractal is sin(x) + sin(2x)/2 + sin(4x)/4 etc then these are more like sin(x) + sin(2x)/4 + sin(4x)/16 etc |