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Clumpy structures are a common feature in X-ray images of young Type Iasupernova remnants (SNRs). Although the precise origin of such clumps remainsunclear there are three generic possibilities: clumpiness imposed during theexplosion, hydrodynamic instabilities that act during the remnant's evolution,and pre-existing structures in the ambient medium. In this article we focus ondiscriminating between clumping distributions that arise from the explosion andthose from the remnant's evolution using existing 3D hydrodynamicalsimulations. We utilize the genus statistic for this discrimination, applyingit to the simulations and {\it Chandra} X-ray observations of the well-known SNIa remnant of SN 1572 (Tycho's SNR). The genus curve of Tycho's SNR stronglyindicates a skewed non-Gaussian distribution of the ejecta clumps and issimilar to the genus curve for the simulation with initially clumped ejecta. Incontrast, the simulation of perfectly smooth ejecta where clumping arises fromthe action of hydrodynamic instabilities produced a genus curve that is similarto a random Gaussian field, but disagrees strongly with the genus curve of theobserved image. Our results support a scenario in which the observed structureof SN Ia remnants arises from initial clumpiness in the explosion.

Genus Statistic Applied to the X-ray Remnant of SN 1572: Clues to the Clumpy Ejecta Structure of Type Ia Supernovae