You don’t need to read the most recent KLM* essay on Self-Similarity to get the full shah-POW of this MWFYW but, dang, I didn’t know about the math-world definition of affine or affinity which then leads to self-affinity till I was doing my research for that essay cuz, wow — they are totally related.

In geometry, according to Mandelbrot (our grandaddy of fractals), self-similarity is the carbon-copy action of “shapes scaling by the same amount in every direction.”

Affine – and onward to affinity then to self-affinity – is just like self-similarity but the carbon-copy action has those shapes scaling in different amounts in only some of its directions. Mandelbrot referred to self-affinity as turbulence.

Self-affinity is turbulent self-similarity.
Now, take my hand (no need to squeeze that hard, sweetie, we’re just talking about mathematics) and let’s look at what’s probably a more familiar usage of this Math WoW for you, as exemplified in this sentence, “I have such an affinity for confident nerds.” Here, affinity means having a particular liking for something or, more often, for a person or people. We commonly use the word affinity in a relational context.

Just as applying self-similarity to real life uncovers how long term processes & systems can arise biases within, self-affinity may be just the thing – that good version of self-similarity – that I was looking for.

A group that has self-affinity rather than self-similarity would be one that has experienced turbulence within as it does that carbon-copy action of scaling. As ‘they’ say , whether you’re part of a couple or a group of people – long-term healthy relationships have disagreements; that’s definitely a type of turbulence.

Groups transform over time – sometimes scaling up and sometimes scaling down. With self-affinity, if you’re realistic about wanting to ensure long term sustainability of that relationship or group, that scaling actually doesn’t – and shouldn’t – scale equally every step of the way.

Huh. Where have you been all my life, affine?