Hi! Thank you for this walk in the space of insects. The spacial complexity implicit in pockets of miniature space seem akin to fractal dimensions or hausdorff dimensions.
Exploring insect space reminds me of my experience exploring non-self-similar 3D fractals, such as hybrid variants of mandleboxes and menger sponges. In these 3D fractals there are fields of complexity and patterns bound to specific scales, and zooming into surfaces would reveal more highly complex space on that surface; branches would “pop up”, and I could rotate my camera around these branches, then zoom into those. And I could repeat this until my zoom level exceeded the floating-point precision offered by by program I was using.
I also see what you mean by the implicit time / energy constraints when moving on surfaces giving extra dimensionality, from the perspective of an insect. Depending on the insect’s locomotion abilities certain surfaces would allow it to move way faster and easier than others, and the differences can be quite stark.
This reminds me of another insight, while thinking about brain-machine interfaces, regarding to how brain neurons are organized: neurons on the cortex / surface of the brain of are highly connected and have a high fractal dimension (~ 2.8 according to wikipedia and the paper it references). As you go deeper into the brain, towards the corpus callosum, this complexity is reduced… axons are longer and tend to be covered with myelin sheath, which increases the conductivity of these connections for longer-running connections. So from the perspective of a neuron in the cortex, neurons way further away can appear closer since the charge and sensitivity requirements between topologically distant neurons are similar to the connections of its neighbors.
As for Worm, I have not read it yet, but the ecological feedback loops being described here is very fun to think about.
Hi! Thank you for this walk in the space of insects. The spacial complexity implicit in pockets of miniature space seem akin to fractal dimensions or hausdorff dimensions.
Exploring insect space reminds me of my experience exploring non-self-similar 3D fractals, such as hybrid variants of mandleboxes and menger sponges. In these 3D fractals there are fields of complexity and patterns bound to specific scales, and zooming into surfaces would reveal more highly complex space on that surface; branches would “pop up”, and I could rotate my camera around these branches, then zoom into those. And I could repeat this until my zoom level exceeded the floating-point precision offered by by program I was using.
I also see what you mean by the implicit time / energy constraints when moving on surfaces giving extra dimensionality, from the perspective of an insect. Depending on the insect’s locomotion abilities certain surfaces would allow it to move way faster and easier than others, and the differences can be quite stark.
This reminds me of another insight, while thinking about brain-machine interfaces, regarding to how brain neurons are organized: neurons on the cortex / surface of the brain of are highly connected and have a high fractal dimension (~ 2.8 according to wikipedia and the paper it references). As you go deeper into the brain, towards the corpus callosum, this complexity is reduced… axons are longer and tend to be covered with myelin sheath, which increases the conductivity of these connections for longer-running connections. So from the perspective of a neuron in the cortex, neurons way further away can appear closer since the charge and sensitivity requirements between topologically distant neurons are similar to the connections of its neighbors.
As for Worm, I have not read it yet, but the ecological feedback loops being described here is very fun to think about.
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refs:
3D fractal rendering software: https://mandelbulber.org/
https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
https://www.sciencedirect.com/science/article/abs/pii/S105381190300380X?via%3Dihub