Self-Similarity: Difference between revisions

Revision as of 07:42, 29 December 2023

Self-similarity and self-reference are key traits of the fractal and therefore the universe.

Self-reference means that recursive algorithms can be used to simplify the process of creating complex patterns. Self-similarity is what you get when you use self-reference and recursion to create a fractal shape.

Without self-similarity and recursion, the coding required to define the structure of a tree or that of our nervous and circulatory systems would be incredibly complex and it becomes impossible to conceive of how these could evolve via random processes. But with it, they boil down to simple branching instructions repeated a few times in a feedback loop.

The macroscopic is a manifestation of the microscopic and the same patterns appear at every level of scale. As the saying goes it's "turtles all the way down".

See Gödel to go down the rabbit hole.

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-[https://en.wikipedia.org/wiki/Self-similarity Self-similarity] is one of the key traits of the [[fractal]] and therefore the [[universe]].
+[https://en.wikipedia.org/wiki/Self-similarity Self-similarity] and [https://en.wikipedia.org/wiki/Self-reference self-reference] are key traits of the [[fractal]] and therefore the [[universe]].
-Self-similarity means that [[recursive]] algorithms can be used to simplify the process of creating complex patterns.
+Self-reference means that [[recursive]] algorithms can be used to simplify the process of creating complex patterns. Self-similarity is what you get when you use self-reference and recursion to create a [[fractal]] shape.
-Without self-similarity and [[recursion]], the coding required to define the structure of a tree or that of our nervous and circulatory systems would be incredibly complex and it becomes impossible to conceive of how these could evolve via random processes. But with it they boil down to simple branching instructions repeated a few times in a [[feedback]] loop.
+Without self-similarity and [[recursion]], the coding required to define the structure of a tree or that of our nervous and circulatory systems would be incredibly complex and it becomes impossible to conceive of how these could evolve via random processes. But with it, they boil down to simple branching instructions repeated a few times in a [[feedback]] loop.
 The macroscopic is a manifestation of the microscopic and the same patterns appear at every level of scale. As the saying goes it's "[https://en.wikipedia.org/wiki/Turtles_all_the_way_down turtles all the way down]".