Molecular dynamics simulations are used to model proteins that diffuse to DNA, 
bind, and dissociate; in the absence of any explicit interaction between 
proteins, or between templates, binding spontaneously induces local DNA 
compaction and protein aggregation. Small bivalent proteins form into rows [as 
on binding of the bacterial histone-like nucleoid-structuring protein (H-NS)], 
large proteins into quasi-spherical aggregates (as on nanoparticle binding), and 
cylinders with eight binding sites (representing octameric nucleosomal cores) 
into irregularly folded clusters (like those seen in nucleosomal strings). 
Binding of RNA polymerase II and a transcription factor (NFκB) to the 
appropriate sites on four human chromosomes generates protein clusters analogous 
to transcription factories, multiscale loops, and intrachromosomal contacts that 
mimic those found in vivo. We suggest that this emergent behavior of clustering 
is driven by an entropic bridging-induced attraction that minimizes bending and 
looping penalties in the template.