Cell-to-cell variation is a universal feature of life that affects a wide range 
of biological phenomena, from developmental plasticity to tumour heterogeneity. 
Although recent advances have improved our ability to document cellular 
phenotypic variation, the fundamental mechanisms that generate variability from 
identical DNA sequences remain elusive. Here we reveal the landscape and 
principles of mammalian DNA regulatory variation by developing a robust method 
for mapping the accessible genome of individual cells by assay for 
transposase-accessible chromatin using sequencing (ATAC-seq) integrated into a 
programmable microfluidics platform. Single-cell ATAC-seq (scATAC-seq) maps from 
hundreds of single cells in aggregate closely resemble accessibility profiles 
from tens of millions of cells and provide insights into cell-to-cell variation. 
Accessibility variance is systematically associated with specific trans-factors 
and cis-elements, and we discover combinations of trans-factors associated with 
either induction or suppression of cell-to-cell variability. We further identify 
sets of trans-factors associated with cell-type-specific accessibility variance 
across eight cell types. Targeted perturbations of cell cycle or transcription 
factor signalling evoke stimulus-specific changes in this observed variability. 
The pattern of accessibility variation in cis across the genome recapitulates 
chromosome compartments de novo, linking single-cell accessibility variation to 
three-dimensional genome organization. Single-cell analysis of DNA accessibility 
provides new insight into cellular variation of the 'regulome'.