thinking about how the explore/exploit dichotomy (ht @ulkar_aghayeva @tszzl) captures the dynamics of our lives, thru the lens of the humble slime mold, physarum polycephalum

we share a fractally-biphasic lifecycle, w/ nested periods of alternating exploration & exploitation

exploration vs exploitation captures a dynamic common to many optimization systems, especially those with a well-defined objective function, operating in a high-dimensional space with local maxima; in such a space, it is not immediately obvious where the best solution lies

depending on the constraints one is operating under, it might be desirable to find a good-enough solution quickly, rather than finding the best-possible; this varies depending on the specifics of the situation. most often, there is a minimum threshold for satisfactory solutions

the primary challenge in these search problems is that it is typically impossible to know a priori whether the local maxima you've found is the global maxima, or if there's a better one out there, & if one invested a bit more into exploration, a better solution would be found

the issue is that, depending on the optimization landscape, it might take more energy to arrive at a better maxima than would make the improvement worthwhile; this is why one must take the specifics of their objective function and properties of their landscape into account

early on in the exploration phase, it is typically advantageous to optimize for optionality, investing energy into creating more possible search avenues, keeping many options open while one searches for higher maxima; this strategy is generally called breadth-first search

at some point tho, its necessary to "commit" & switch to exploitation mode, whatever that entails for your objective; could be anything from picking a partner, accepting a job offer, or even deciding which bagel place to go to. might always be a better one out there, but so what?

in exploitation mode, you're no longer searching but actively "using" your result; interestingly enough, this itself often presents new optimization problems! sure, you've chosen a bagel place, but which combination of toppings is best? time to explore the bagel topping space!

with many real-world optimization problems, there are many levels of decisions which need to be made, especially in domains with hidden dimensions, ie, factors which are local rather than global; different bagel places might have different topping options!

this is what is meant by a fractally-biphasic lifecycle; the optimization algorithm is self-similar, in that exploitation phases themselves contain smaller instances of the explore/exploit problem! depending on the nature of the optimization landscape, these can be deeply nested

thats cool and all, but what's the relationship to slime molds?

these organisms are rather primitive, being multinucleated acellular protists, often compared to fungi but much closer to amoebas. of primary interest here is the behavior of the plasmodium stage, how it seeks food

the slime mold expands and contracts its membrane, causing its cytoplasm to flow into certain regions, expanding it outwards in those directions; if it detects food it grows around it, consuming it and expanding, but if not, it contracts away from that region, leaving markers

through the 100 second period of these pulsations, the slime mold is effectively exploring its surroundings, executing a sort of physical breadth-first search. once it finds food, it builds "channels", tube-like structures enabling easier transport, and then it repeats.

here's the fun part: out of this very simple behavior emerges a form of intelligence; the slime mold is able to solve shortest-path problems! over many iterations, we see slime molds construct efficient and resilient networks of tubes between food clusters, on par w/ human algos!