We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit .
The simulation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster and , simultaneously , the formation of circumstellar discs and binary stars .
This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations .

The calculation clearly demonstrates that star formation is a highly-dynamic and chaotic process .
Star formation occurs in localised bursts within the cloud via the fragmentation both of dense molecular cloud cores and of massive circumstellar discs .
Star-disc encounters form binaries and truncate discs .
Stellar encounters disrupt bound multiple systems .
We find that the observed statistical properties of stars are a natural consequence of star formation in such a dynamical environment .
The cloud produces roughly equal numbers of stars and brown dwarfs , with masses down to the opacity limit for fragmentation ( \approx 5 Jupiter masses ) .
The initial mass function is consistent with a Salpeter slope ( \Gamma = -1.35 ) above 0.5 M _ { \odot } , a roughly flat distribution ( \Gamma = 0 ) in the range 0.006 - 0.5 M _ { \odot } , and a sharp cutoff below \approx 0.005 M _ { \odot } .
This is consistent with recent observational surveys .
The brown dwarfs form by the dynamical ejection of low-mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses .
Close binary systems ( with separations \mathrel { \hbox { \hbox to 0.0 pt { \lower 2.365 pt \hbox { $ \sim$ } } \kern - 3.0 pt \raise 1.72 pt \hbox { $ < $ } } } 10 AU ) are not formed by fragmentation in situ .
Rather , they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters , gas accretion , and/or the interaction with circumbinary and circumtriple discs .
Finally , we find that the majority of circumstellar discs have radii less than 20 AU due to truncation in dynamical encounters .
This is consistent with observations of the Orion Trapezium Cluster and implies that most stars and brown dwarfs do not form large planetary systems .