Space-filling tree | Wikipedia audio article
Channel: wikipedia tts
Date: 03/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Space-filling_tree


00:00:55 1 Definition
00:03:13 2 Examples
00:05:02 3 See also



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Speaking Rate: 0.8364888320252858
Voice name: en-AU-Wavenet-B


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- Socrates


SUMMARY
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Space-filling trees are geometric constructions that are analogous to space-filling curves, but have a branching, tree-like structure and are rooted.  A space-filling tree is defined by an incremental process that results in a tree for which every point in the space has a finite-length path that converges to it. In contrast to space-filling curves, individual paths in the tree are short, allowing any part of the space to be quickly reached from the root.
 The simplest examples of space-filling trees have a regular, self-similar, fractal structure, but can be generalized to non-regular and even randomized/Monte-Carlo variants (see Rapidly exploring random tree).  Space-filling trees have interesting parallels in nature, including fluid distribution systems, vascular networks, and fractal plant growth, and many interesting connections to L-systems in computer science.