Are the imprints left by repeated interactions more akin to erosion of a surface, formation of a stalactite by material being left behind as water flows through, or formation of stalagmite at the terminal end of the waters path? These all seem like distinct types of results of repetitive action but I don't know if any fit

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The delta interaction is the simplest type of interaction, and combinations of them (convolutions) can approximate any type of more complex interaction. Theres an animation here to help explain.

https://wikistr.com/delta-interaction*dc4cd086cd7ce5b1832adf4fdd1211289880d2c7e295bcb0e684c01acee77c06

Also stems from the main argument of Semiotic Interaction

https://wikistr.com/semiotic_interaction*dc4cd086cd7ce5b1832adf4fdd1211289880d2c7e295bcb0e684c01acee77c06