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Next comes this: > "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos

Next comes this: > "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." Yeah, real life is not a computer simulation (AFAIK), and thus is not made "of randomly dispersed dots"

eternalban 3y ago
They were referring to this distinction: "Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space." - D'ary Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/On_Growth_and_Form https://en.wikipedia.org/wiki/On_Growth_and_Form
- anigbrowl 3y ago
  This may be true even for inorganic matter, eg cracks in dried mud follow a predictable development that can be modeled quite economically. http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf
ska 3y ago
> "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." That one is kind of silly, because while the chaos game is one way to realize an IFS like the Barnsley fern, there are others that are more geometric. For example specifically in that case, you can iterate any closed set in the plane under the contractive mapping that defines it, and you will end up converging to the set. Nothing chaotic about that. The algorithm they are referring to (chaos game) does it pointwise which is easier in a computer, but relies on the fact that the resultant sequence of points will, at least after a while, stay distributed over a probability measure supported by the set.

eternalban 3y ago

They were referring to this distinction: "Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space." - D'ary Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/On_Growth_and_Form https://en.wikipedia.org/wiki/On_Growth_and_Form

anigbrowl 3y ago
This may be true even for inorganic matter, eg cracks in dried mud follow a predictable development that can be modeled quite economically. http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf

ska 3y ago

> "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." That one is kind of silly, because while the chaos game is one way to realize an IFS like the Barnsley fern, there are others that are more geometric. For example specifically in that case, you can iterate any closed set in the plane under the contractive mapping that defines it, and you will end up converging to the set. Nothing chaotic about that. The algorithm they are referring to (chaos game) does it pointwise which is easier in a computer, but relies on the fact that the resultant sequence of points will, at least after a while, stay distributed over a probability measure supported by the set.