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Particle systems are inherently history dependent. In other words, to be able to determine the state of a particle system at, say, frame 100, the software has to calculate the states for all previous frames since the first particle is born. This is because the changes in particle properties - for example, the positions of the particles - accumulate due to the constant changes in other parameters, such as speed.
However, for particular setups some particle properties are not history dependent, and can be calculated from the current state of the particles. For example, the orientation of the particles if they "look at" something such as the camera, or follow particle speed. Here the orientation of the particle depends either on particle position, as is the case when facing the camera, or particle speed. In this case, to calculate the current orientation of the particles, you don't need to know the entire history of the particles; you just need to know their current speed or position.
In that sense, the operator that calculates particle orientation is not history dependent. The operator does not have to do anything while the system runs through all prior frames in order to get to the current frame. The operator has to work only on the final frame; to analyze the position/speed of the particles in the final frame and calculate the corresponding particle orientation.
In this animation (2.4MB) three PFlow systems are used to simulate "hydraulic restraints" for an animated blob. Particles are fixed in 3D space and are oriented to look at the closest point of the blob surface. The overall "Look At" setup does not need to calculate history dependent properties of particles. Therefore it is possible to jump to an arbitrary frame right away. This is why in all Output sub-operators the History-Dependent option is turned Off. Also, all Output sub-operators are set to Post, therefore all calculations are done after the animated blob surface has settled. This way the placement of the closest-point balls is more precise.
