= Minkowski sausage
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{title2=$\dim_HF=\log8/\log4=3/2$}
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The <Minkowski sausage> replaces a segment by eight directed unit segments whose endpoint displacement is four units. A middle straight run of length two represents two collinear unit segments. After normalizing the displacement to one, the eight <contracting Euclidean similarities> all have ratio $1/4$. The open diamond $\{|x-1/2|+|y|<1/2\}$ is an <open set condition> witness: its eight image diamonds have disjoint interiors and lie within it. Hence $8(1/4)^s=1$, giving <Hausdorff dimension> $3/2$. Treating the middle run as a single similarity of ratio $1/2$ instead defines a different iterated scheme.
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