The Cartographer draws its realms from a seeded fBm heightmap whose roughness slider is the noise's persistence. Its coast is the line where that height crosses sea level. Here we take that exact coast and ask Richardson's 1961 question: how long is it?
Measure with a smaller ruler and the answer keeps growing — that's the paradox. The growth rate is a fractal dimension D, and we measure it two unrelated ways that must agree.
Higher gain keeps more fine detail ⇒ a crinklier coast. In theory the level set of an fBm has dimension D = 2 − H with H = −log₂(gain).
Box-counting tiles the plane with boxes of side ε and counts those the coast touches: N(ε) ∝ (1/ε)D. The divider walks the shore with a compass of opening ε; the length L(ε) ∝ ε1−D diverges. Two methods, no shared code — they land on the same D.
The slider's predicted 2−H is the idealized fBm value; the real realm is warped, masked & islanded, so the measured D runs tamer — but tracks the slider, and lands right where real coasts do (D≈1.15–1.25).