https://apm.bplaced.net/w/index.php?action=history&feed=atom&title=Scale_invariance 2026-04-20T17:14:05Z Revision history for this page on the wiki MediaWiki 1.43.0 https://apm.bplaced.net/w/index.php?title=Scale_invariance&diff=19679&oldid=prev 2026-03-29T20:38:15Z

<p><a href="/w/index.php?title=Category:Surprising_facts" title="Category:Surprising facts">Category:Surprising facts</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:38, 29 March 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20">Line 20:</td> <td colspan="2" class="diff-lineno">Line 20:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Convergent assembly]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Convergent assembly]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Log polar mapping]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [[Log polar mapping]]</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Surprising facts]]</ins></div></td></tr> </table>

Apm https://apm.bplaced.net/w/index.php?title=Scale_invariance&diff=16201&oldid=prev 2024-03-01T08:06:46Z

<p>basic page</p> <p><b>New page</b></p><div>{{stub}}<br /> When some geometry is scaled up/down by a certain constant factor then it maps to a geometry that is indistinguishable form the original geometry. &lt;br&gt;<br /> This is similar to translational symmetry in the sense that logarithmic mapping of the geometry leads to translational symmerty. &lt;br&gt;<br /> See: [[Log polar mapping]]<br /> <br /> Fractal self similarity across scales can (but may not) be a weaker property. &lt;br&gt;<br /> Like the Mandelbrot set is not scale invariant in the stringent sense stated above. &lt;br&gt;<br /> Scale invariance needs to hold only for the local limit with more or less of the surroundings. &lt;br&gt;<br /> There are truly scale invariant fractals with branching that goes beyond what&#039;s possible in layers in 3D. &lt;br&gt;<br /> {{wikitodo|Add an example and explain why layers are a more natural baseline model fro productive nanosystems.}}<br /> <br /> In [[advanced productive nanosystems]] like [[gem-gum factories]] there may be some limited form of cale invariance. &lt;br&gt;<br /> Especially when organized in [[assembly layers]]. An especially for the upper end of the [[Convergent assembly]]. &lt;br&gt;<br /> Bottom layers must feature heavy deviations from scale invariant geometry due to a number of factors. &lt;br&gt;<br /> Some explained on page: [[Convergent assembly]].<br /> <br /> == Related ==<br /> <br /> * [[Higher throughput of smaller machinery]]<br /> * [[Convergent assembly]]<br /> * [[Log polar mapping]]</div>

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