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We studied the invariant fractals in convex N-gons given by N identical pure contractions at its vertices with non-overlapping images, which we called uniform Sierpinski fractals. We provided the explicit formulae for the maximal contraction ratio RN, and the maximal Hausdorff dimension hN, for the uniform Sierpinski fractals. We used maximal N-grams and principal crossing points as the main tools.

A 62-year-old female presented with a linear arrangement of multiple asymptomatic, discrete, dome-shaped, smooth, skin-colored papules and nodules involving the left forehead. Histopathology showed a poorly circumscribed nodule of haphazardly arranged fascicles of smooth muscle cells involving the papillary and superficial reticular dermis. Genetic testing revealed the patient to be heterozygous for the R233H mutation in the fumarate hydratase gene. Clinical, microscopic, and genetic findings were consistent with a diagnosis of Reed syndrome. Reed syndrome is a rare disorder defined by cutaneous and uterine leiomyomas and, uncommonly, renal cell carcinoma.