Recent progress in the simulation of supernovae (SNe) has shown the importance of turbulence and asymmetries in successful explosions, which prompts us to revisit the subsequent phase, the supernova remnant (SNR). Can we use the SNR morphology as a probe of the explosion mechanism? Recent work has shown the interest of this approach for a core-collapse SNR like Cas A. Here we argue for the case of a Type Ia SNR like Tycho. Our project is making the link between two communities, the one studying the explosion and the one studying the remnant. We have run 3D simulations of a SNR starting from the output of a 3D simulation of the thermonuclear explosion of a Chandrasekhar-mass white dwarf. By analyzing the wavefronts we have quantified the imprint of the explosion on the remnant over time. Assuming a uniform ambient medium, we find that the impact of the SN on the SNR may still be visible after hundreds of years. And interestingly, the newly simulated maps look more realistic than in previous works based on spherically symmetric ejecta profiles.