The dispersion method of impact attentuation can best be described as a surface scattering when impacted by something, implying that this cannot be achieved with anything solid or unitary in structure. Dispersion is commonly exhibited with water impacts, and others include sand, pea gravel or other what are termed loose-fill particles, and the effectiveness is determined by the size, shape and consistency of the particulates, their density and other physical properties.
Impact attenuation could be described as the rapid and gradual decelleration of a moving object, absorbing the kinetic energy upon impact. The movie industry uses massive 1 to 2 story thick airbags shaped like mattresses, with velcro flaps that open to release some of the inside air upon impact to gradually reduce the speed and rate of descent until fully stopped, to keep stunt people safe from high elevation falls. It's a great form of fall protection that's hardly practical and adaptable to daily life, or real life scenarios effectively and efficiently.
The materials that are most commonly utilized for playground fall safety surfacing are either monolithic or unitary, or loose-fill in nature, with loose-fill tending to provide better impact attentuation. Part of this is due to the physics involved where the amount of dispersion varies depending on the velocity and mass of the impacting body, together with all the elements that define a loose-fill surfaces effectiveness.
Part of what makes our rubber mulch so effective and safe for fall impact injury protection is it initially uses the dispersion method to cause brief decelleration before the secondary compression method brings the impacting body to a stop, without returning to its original position, thereby completely absorbing the kinetic energy of an impact the best.