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Agreed. I’m not a biologist, but I always assumed the self similarity of plants and trees is definitely some recursive process with some boundary conditions or

Agreed. I’m not a biologist, but I always assumed the self similarity of plants and trees is definitely some recursive process with some boundary conditions or external constraints as an implicit parametrization. Which is very similar to how you can describe (some) fractals. It feels very unlikely to me that the tree dna for thick branches is completely different from that for thin twigs.

EamonnMR 3y ago
The thick branches, of course, start out as thin twigs.
RosanaAnaDana 3y ago
It's really not that complicated. all vascular plants have basically the same node -- axially meristem -- internode -- node pattern to growth. All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. It's also why it's so easy to effectively take cuttings and get a an 'fully mature' plant from them (eventually). Every node--etc.. section is the same pattern as every other. It's largely due to the exogenous origin of branching.
- robotresearcher 3y ago
  > All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. > Every node--etc.. section is the same pattern as every other. Common sense says this isn't true. Some sections grow leaves and flowers rather than smaller branches, others do not.
  - ksaj 3y ago
    It boils down to an if statement. Once you've reached a certain number of iterations, or the initial branching meets certain conditions, another rule set applies. But those rules are still not all that different - follow the leaf veins, and all their branching throughout. The same applies to the roots.
    - robotresearcher 3y ago
      The article denies that, at least for the species and structures it discusses. It specifically says it's a non iterative process. That's the point the paper is trying to make. I'm not sure if that's the structures you are talking about, but a few comments up declared 'All plants are actually fractals'. The paper says no, at least in the aspects they are talking about, which are structures that appear fractal-like but are not. They also say it's misleading to think of them as fractals, as the processes are importantly different.
- Clamchop 3y ago
  Not all plants have the growth patterns you describe. Many monocots and gymnosperms (cycads) either don't branch, or do so irregularly (they'll look "messy", think Joshua trees or branching palms), and cuttings aren't a viable means of propagation. Whatever the definition of a fractal (seems contentious), these plants aren't clearing the bar.
ksaj 3y ago
Yes indeed. Without boundary conditions, they would grow indefinitely. Imagine a 3 story (and growing) cauliflower. There are fractals that simulate tree growth. Even they have boundaries to stop them from turning into a giant fuzzy ball. Also, unlike mathematical fractals, nature has limits as to how tiny things can be. At some point, it becomes quantum effects rather than fractal ones. Fractal math doesn't usually bother with that distinction, and will happily drive towards an infinitely small point, which in nature would be meaningless. Hell, even we can only appreciate mathematical fractals if we zoom in digitally, meaning the numbers are reset to larger quantities than they were before the zoom. That effectively makes the digital zoom a bit of a mirage. Nature doesn't ever have to do that, because of natural constraints. Once you reach the quantum level, things start to look really similar to each other, which never seems to be considered in mathematical fractals.

EamonnMR 3y ago

The thick branches, of course, start out as thin twigs.

RosanaAnaDana 3y ago

It's really not that complicated. all vascular plants have basically the same node -- axially meristem -- internode -- node pattern to growth. All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. It's also why it's so easy to effectively take cuttings and get a an 'fully mature' plant from them (eventually). Every node--etc.. section is the same pattern as every other. It's largely due to the exogenous origin of branching.

robotresearcher 3y ago
> All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. > Every node--etc.. section is the same pattern as every other. Common sense says this isn't true. Some sections grow leaves and flowers rather than smaller branches, others do not.
- ksaj 3y ago
  It boils down to an if statement. Once you've reached a certain number of iterations, or the initial branching meets certain conditions, another rule set applies. But those rules are still not all that different - follow the leaf veins, and all their branching throughout. The same applies to the roots.
  - robotresearcher 3y ago
    The article denies that, at least for the species and structures it discusses. It specifically says it's a non iterative process. That's the point the paper is trying to make. I'm not sure if that's the structures you are talking about, but a few comments up declared 'All plants are actually fractals'. The paper says no, at least in the aspects they are talking about, which are structures that appear fractal-like but are not. They also say it's misleading to think of them as fractals, as the processes are importantly different.
Clamchop 3y ago
Not all plants have the growth patterns you describe. Many monocots and gymnosperms (cycads) either don't branch, or do so irregularly (they'll look "messy", think Joshua trees or branching palms), and cuttings aren't a viable means of propagation. Whatever the definition of a fractal (seems contentious), these plants aren't clearing the bar.

ksaj 3y ago

Yes indeed. Without boundary conditions, they would grow indefinitely. Imagine a 3 story (and growing) cauliflower. There are fractals that simulate tree growth. Even they have boundaries to stop them from turning into a giant fuzzy ball. Also, unlike mathematical fractals, nature has limits as to how tiny things can be. At some point, it becomes quantum effects rather than fractal ones. Fractal math doesn't usually bother with that distinction, and will happily drive towards an infinitely small point, which in nature would be meaningless. Hell, even we can only appreciate mathematical fractals if we zoom in digitally, meaning the numbers are reset to larger quantities than they were before the zoom. That effectively makes the digital zoom a bit of a mirage. Nature doesn't ever have to do that, because of natural constraints. Once you reach the quantum level, things start to look really similar to each other, which never seems to be considered in mathematical fractals.