Our genetic material is packed into the nucleus of the cell, but is the packing process random or organized in some way? In a recent study published in Cell Stem Cell, Krijger et al. showed predictable 3D arrangements of chromosomal regions in the nucleus. These structures were effectively erased when more mature cells were reprogrammed to undifferentiated stem cells. But intriguingly, the undifferentiated stem cells, reprogrammed from different mature cell types, acquired new topological features dependent on the starting founder cell-type. Thus, a memory of nuclear organization influences the trajectory of nuclear rearrangements in the reprogramming process.