HackerFractals are typically not self-similar
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Caption notes
Cover a coastline with progressively finer grids and count the occupied boxes. A log-log slope estimates a scaling law; the fitted value on finite data can depend on the range examined.
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What this suggests is that if you were to plot the log of the scaling factor against the log of the number of boxes touching the coastline, the relationship should look like a line, and that line should have a slope equal to the dimension.this dimension, at least as I've described it so far using the box counting method, can sometimes change based on how far zoomed in you are.