If you have data about when people joined an org, changed managers, and left, you can generate an animated historical org chart. You can see a sample or clone this repo and open index.html. To supply your own org chart, replace the data in org_history.js.
On index.html you can use the left and right arrows to move through time. Or you can click on the the circles in the timeline at the bottom of the visualization. (The org chart starts at the current state of the org which may not be the right most point on the timeline if your data includes forward-looking reorgs.)