Histone modifications can redistribute along the genome in a sequenceindependent manner, giving rise to chromatin position effects and epigenetic memory. The underlying mechanisms shape the endogenous chromatin landscape and determine its response to ectopically targeted histone modifiers. Here, we simulate linear and loopingdriven spreading of histone modifications and compare both models to recent experiments on histone methylation in fission yeast. We find that a generalized nucleation-and-looping mechanism describes key observations on engineered and endogenous methylation domains including intrinsic spatial confinement, independent regulation of domain size and memory, variegation in the absence of antagonists, and coexistence of short-and long-term memory at loci with weak and strong constitutive nucleation. These findings support a straightforward relationship between the biochemical properties of chromatin modifiers and the spatiotemporal modification pattern. The proposed mechanism gives rise to a phase diagram for cellular memory that may be generally applicable to explain epigenetic phenomena across different species.epigenetic memory | heterochromatin | epigenome editing | histone modification | stochastic simulation H istone posttranslational modifications regulate cellular processes including gene expression, DNA replication, and DNA repair (1, 2). Some of these modifications can spread along the genome independently of the underlying DNA sequence, forming extended domains of modified histones. Well-known examples are di/trimethylation of histone 3 at lysine 9 (H3K9me2/3) and at lysine 27 (H3K27me2/3), which are enriched in heterochromatin and play a role in gene silencing (3-5). H3K9me2/3 can spread around centromeres (6) and telomeres (7), and H3K27me2/3 can spread around dedicated response elements within the genome (8, 9), causing socalled chromatin position effects by repressing genes within the methylated domains (7, 10, 11). The enzymes that are responsible for heterochromatic H3K9me2/3 are Clr4 in fission yeast and Suv39h in metazoans, and the PRC2 complex catalyzes H3K27me2/3 (12). By stably tethering these enzymes to chromatin, extended engineered domains enriched for the respective modification can be formed (13)(14)(15)(16)(17)(18)(19)(20). Furthermore, both modifications can confer epigenetic memory at least across several cell divisions (14)(15)(16)(17)21).Aberrations in histone modification patterns and the responsible enzymes are involved in several diseases, including cancer (22, 23). It has recently become possible to recruit histone-modifying enzymes to endogenous target sites, e.g., by using the CRISPR-Cas9 system, thereby eliciting programmed changes to histone modifications and triggering specific position effects (24,25). Due to the functional relevance of the chromatin landscape, this technique holds promise for future clinical applications (26,27). Therefore, it is particularly important to understand if and how far modifications can spread and how long engineered domains a...