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"Like fern leaves or any other plant branching system at the organ level, the cauliflower curd develops from the inside out through a process totally different

"Like fern leaves or any other plant branching system at the organ level, the cauliflower curd develops from the inside out through a process totally different from fractal drawing." Soooo, what the author is stating is they are actually even more amazing and wonderfully made than we originally thought. Even though they look like the mathematical model of a built fractal they grow entirely different and with an internal program that cannot be reproduced by our existing knowledge-base.

jonathankoren 3y ago
I read that same line, but came to the opposite conclusion than you. I didn’t find it amazing at all, instead I found it banal. Essentially the author is saying that fern leaf doesn’t grow as single line, and then subdivides. Well, no shit. Literally no one ever thought that. It betrays a lack of imagination where the author is conflating a single algorithm for the construction of a fractal to an actual fractal shape. It’s the same as complaining that something similar to a Sierpinski’s Triangle can’t be a fractal because it wasn’t made by placing atoms at the midpoints between it and a randomly selected exterior vertex. Are fern leaves technically fractals? No. (And no, I am not talking about the sophomoric objection then lacking infinite regression.) Are they similar to fractals? Yes. Is it useful as an illustration of both a feactal, and how complex body plans can be encoded in DNA without actually specifying every point like a literal blueprint? Yes. None of this is different than the discussing the similarities fractals and coastlines. No one thinks Britain is a literal fractal. Honestly, this idea of fractals is very similar to the idea that the irrational number phi shows up it nature. When you actually look deeply at the purported examples, you’ll find out, it’s not actually there.
ajuc 3y ago
You can create the same fractal in many ways. For example you get Sierpiński triangle if you repeatedly draw smaller triangles, or you can just do xor.
- CrazyStat 3y ago
  My favorite way to draw the Sierpinski triangle is Monte Carlo: 1. Pick a point which is in the triangle (e.g. one of the corners of the triangle). Draw that point. 2. Choose one corner of the triangle at random. 3. Move to the point half way between your current point and the chosen corner. Draw that point. 4. Repeat steps 2-3 as long as desired. Obviously this only ever reaches a countable subset of the triangle based on where you start, but that subset is everywhere dense in the triangle so it doesn't matter. You can also start at an arbitrary point that's not actually in the triangle. If you discard the first k (say 10) iterations you'll still get something visually indistinguishable from a Sierpinski triangle. You can also do this with other self-similar fractals, you just have to find the right set of transformations to use. It's quite fun watching the random points coalesce into the shape of the fractal.
  - ska 3y ago
    These sets of transforms are known as iterated function systems (IFS), and the algorithm dubbed "the chaos game" by Barnsley. If I recall correctly the algorithm actually distributes uniformly over a probability measure supported by the set, so for picture-making purposes it is typically done with a probability associated with each transforms chosen to even out the visitation (otherwise some details will take forever to be seen). The whole area is a consequence of Banach's fixed point principle (a very fundamental result), with Hutchinson I think extending it to unions of contractive maps. Math has many beautiful corners.
dekhn 3y ago
Generative processes in biology are complex and fascinating. A lot of modelling builds simpler models which can be analyzed but don't explicitly simulate the full process of growth and development (which would require extreme memory and CPU). There is an open question in the field about how closely models need to recapitulate the underlying biology to be useful (in terms of generalized predictive ability). Some interesting reading on development and math modelling: https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_system https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_sys... https://en.wikipedia.org/wiki/Multi-state_modeling_of_biomolecules https://en.wikipedia.org/wiki/Multi-state_modeling_of_biomol... https://en.wikipedia.org/wiki/Pattern_formation https://en.wikipedia.org/wiki/Pattern_formation When I was growing up, and until not too much longer ago, I assumed it would be practical to build full molecular dynamic simulations with atomic or quantum details, simulating large systems like groups of cells. Now I appreciate that this would be a lot of work that could be better handled by a well-trained deep neural net whose model does not recapitulate the underlying mechanics.

jonathankoren 3y ago

I read that same line, but came to the opposite conclusion than you. I didn’t find it amazing at all, instead I found it banal. Essentially the author is saying that fern leaf doesn’t grow as single line, and then subdivides. Well, no shit. Literally no one ever thought that. It betrays a lack of imagination where the author is conflating a single algorithm for the construction of a fractal to an actual fractal shape. It’s the same as complaining that something similar to a Sierpinski’s Triangle can’t be a fractal because it wasn’t made by placing atoms at the midpoints between it and a randomly selected exterior vertex. Are fern leaves technically fractals? No. (And no, I am not talking about the sophomoric objection then lacking infinite regression.) Are they similar to fractals? Yes. Is it useful as an illustration of both a feactal, and how complex body plans can be encoded in DNA without actually specifying every point like a literal blueprint? Yes. None of this is different than the discussing the similarities fractals and coastlines. No one thinks Britain is a literal fractal. Honestly, this idea of fractals is very similar to the idea that the irrational number phi shows up it nature. When you actually look deeply at the purported examples, you’ll find out, it’s not actually there.

ajuc 3y ago

You can create the same fractal in many ways. For example you get Sierpiński triangle if you repeatedly draw smaller triangles, or you can just do xor.

CrazyStat 3y ago
My favorite way to draw the Sierpinski triangle is Monte Carlo: 1. Pick a point which is in the triangle (e.g. one of the corners of the triangle). Draw that point. 2. Choose one corner of the triangle at random. 3. Move to the point half way between your current point and the chosen corner. Draw that point. 4. Repeat steps 2-3 as long as desired. Obviously this only ever reaches a countable subset of the triangle based on where you start, but that subset is everywhere dense in the triangle so it doesn't matter. You can also start at an arbitrary point that's not actually in the triangle. If you discard the first k (say 10) iterations you'll still get something visually indistinguishable from a Sierpinski triangle. You can also do this with other self-similar fractals, you just have to find the right set of transformations to use. It's quite fun watching the random points coalesce into the shape of the fractal.
- ska 3y ago
  These sets of transforms are known as iterated function systems (IFS), and the algorithm dubbed "the chaos game" by Barnsley. If I recall correctly the algorithm actually distributes uniformly over a probability measure supported by the set, so for picture-making purposes it is typically done with a probability associated with each transforms chosen to even out the visitation (otherwise some details will take forever to be seen). The whole area is a consequence of Banach's fixed point principle (a very fundamental result), with Hutchinson I think extending it to unions of contractive maps. Math has many beautiful corners.

dekhn 3y ago

Generative processes in biology are complex and fascinating. A lot of modelling builds simpler models which can be analyzed but don't explicitly simulate the full process of growth and development (which would require extreme memory and CPU). There is an open question in the field about how closely models need to recapitulate the underlying biology to be useful (in terms of generalized predictive ability). Some interesting reading on development and math modelling: https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_system https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_sys... https://en.wikipedia.org/wiki/Multi-state_modeling_of_biomolecules https://en.wikipedia.org/wiki/Multi-state_modeling_of_biomol... https://en.wikipedia.org/wiki/Pattern_formation https://en.wikipedia.org/wiki/Pattern_formation When I was growing up, and until not too much longer ago, I assumed it would be practical to build full molecular dynamic simulations with atomic or quantum details, simulating large systems like groups of cells. Now I appreciate that this would be a lot of work that could be better handled by a well-trained deep neural net whose model does not recapitulate the underlying mechanics.