Visual Math / Fractals


	Visual Math / Fractals
CrazyRedHead
2-29-2008 9:11 PM
1263 views
tags:
science, mathematics, fractals, art
CrazyRedHead says:
An introduction to the fascinating patterns of Visual Math - many more drawings and diagrams at the site.
4 Comments |
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3-1-2008 3:28 AM
alanocu
nice clip!
3-1-2008 10:12 AM
AcesLucky
excellent !
3-2-2008 5:53 AM
papananook
Very pschedelic...my son turned me on to fractals when he was studying physics and chaos theory. popity-pop
3-6-2008 2:52 AM
merrie
nice fractals thanks CRH
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<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/acb3b091-c593-4619-ba55-2603fc3ba427/91666345-738E-4402-B0FF-90EC57BCAD6F/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/www.miqel.com/img/46A38C3E-74E2-4AD4-9DAF-D42376B3974E" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html">Sierpinski Triangle</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/09E20FAE-AA34-457F-BFFF-FB7BC99E05E5" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html"><FONT size="2" face="Arial, Helvetica, sans-serif" color="#006699">honeycomb 
                      fractal branching structure</FONT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/B8C2AFE3-42B6-4EC5-BB11-3C36F587EEB0" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html"><FONT size="2" color="#006699"> 
                      The Apollony fractal </FONT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.miqel.com/img/6EE7E691-D14B-4A38-BC24-83DBC42B909D" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-iterative-fractals.html">Dodecahedral 
                      Fractal</blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content9.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/23C5C1B8-2839-4FF6-ADC8-A39EDA57A64C" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html"><FONT size="4" face="Verdana, Arial, Helvetica, sans-serif" color="#006699">Naturally 
                        Occurring Fractals</FONT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/892BCFAE-9BD6-49CC-8317-B55C59A84380" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.miqel.com/img/955E6AA2-98B5-4E85-A1AC-FD0D5E5A1407" alt="" /></div></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content9.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-minimal-surfaces.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-minimal-surfaces.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-minimal-surfaces.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/EF22F85F-65CB-4BC9-AFD4-650E1D795C35" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-minimal-surfaces.html"><FONT size="4" face="Verdana, Arial, Helvetica, sans-serif" color="#006699">Minimal 
                        Surfaces and Geodesic Forms</FONT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-minimal-surfaces.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/63FA7CD3-5610-47C8-80BE-6783A7249387" alt="" /></div></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content8.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/www.miqel.com/img/7FBC1E9D-CBCA-4CD8-85FF-C0AF1914DC01" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html">The Golden Ratio </blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.miqel.com/img/7243C2E8-844C-4C20-B0A0-3ED9C69BDBB6" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html"><STRONG>Phi 
                            and the MANDELBROT SET</STRONG></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content9.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/B3A236DF-09BF-44F9-9244-67B86B79F66B" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html">the 
                        Mandelbrot set, perhaps the most famous Fractal</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/F91746D4-8955-4A95-A318-8368E92E98F1" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.miqel.com/img/8D900B1F-DF41-4AAD-AC8D-AF872FD662E7" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-mandelbrot-magic.html"> View of some of the Interior Relationships in the Mandelbrot 
                      Set</blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content9.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/924B8C1E-F190-44C5-91B3-D53A7A7D4404" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><FONT size="4" face="Verdana, Arial, Helvetica, sans-serif" color="#006699">Reflective 
                      Spheres of Infinity: Wada Basin Fractals</FONT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><B>the infinite series of inter-reflections when mirrored 
                      spheres
</B>(such as christmas ornaments)<B> are packed together.</B></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/039C451C-9A8D-46C8-BAAE-0ABFE09063E9" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.miqel.com/img/F40E664F-6E2B-4563-9AC1-0F1787778135" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/BFFFCA8C-7C97-4ACB-AD4D-ABEDA11D1034" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-wada-basin-spheres.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/440DD506-F55E-4516-A41F-FF2E2230DECF" alt="" /></div></blockquote><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content8.clipmarks.com/images/clip-icon.gif" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html" href="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html" style="font-size: 11px;">www.miqel.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html"><FONT size="4" face="Verdana, Arial, Helvetica, sans-serif" color="#006699">Platonic 
                        / Vectoral Geometry</FONT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.miqel.com/img/519A0FEF-5753-4935-817C-A646FB89D5D1" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.miqel.com/img/1967C65D-065D-45E0-BE66-FCF7C607C8AA" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/www.miqel.com/img/285DE71C-3EFB-4CA2-89D3-0D8237FAFFA2" alt="" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html">fascinating 
                      patterns can be created by simple repetition,
such as decreasing the scale while twisting the angle -
to create this cubical vortex or the hexagonal regress below</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.miqel.com/fractals_math_patterns/visual-math-platonic.html"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.miqel.com/img/410A0532-0256-46EA-8E10-A3C42889DF5C" alt="" /></div></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/91666345-738E-4402-B0FF-90EC57BCAD6F/blog/" title="blog or email this clip"><img src="http://content7.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>
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