Clumpy structures are a common feature in X-ray images of young Type Ia supernova remnants (SNRs). Although the precise origin of such clumps remains unclear, there are three generic possibilities: dumpiness imposed during the explosion, hydrodynamic instabilities that act during the remnant's evolution, and preexisting structures in the ambient medium. In this article we focus on discriminating between clumping distributions that arise from the explosion and those from the remnant's evolution using existing 3D hydrodynamical simulations. We utilize the genus statistic for this discrimination, applying it to the simulations and to Chandra X-ray observations of the wellknown SN Ia remnant of SN 1572 (Tycho's SNR). The genus curve of Tycho's SNR strongly indicates a skewed non-Gaussian distribution of the ejecta clumps and is similar to the genus curve for the simulation with initially clumped ejecta. In contrast, the simulation of perfectly smooth ejecta where clumping arises from the action of hydrodynamic instabilities produced a genus curve that is similar to a random Gaussian field, but disagrees strongly with the genus curve of the observed image. Our results support a scenario in which the observed structure of SN Ia remnants arises from initial dumpiness in the explosion.