  A minor-closed class of matroids is (strongly) fractal if the number of
n-element matroids in the class is dominated by the number of n-element
excluded minors. We conjecture that when K is an infinite field, the class of
K-representable matroids is strongly fractal. We prove that the class of sparse
paving matroids with at most k circuit-hyperplanes is a strongly fractal class
when k is at least three. The minor-closure of the class of spikes with at most
k circuit-hyperplanes (with k>4) satisfies a strictly weaker condition: the
number of 2t-element matroids in the class is dominated by the number of
2t-element excluded minors. However, there are only finitely many excluded
minors with ground sets of odd size.
