I know this post seems simple, but the benefits are profound for anyone who uses a computer regularly.
Using computers for long periods keeps us in a relatively fixed position, causing strain on our bodies. Our bodies were meant to be in a dynamic state, even when standing we naturally shift positions. When sleeping, if sleeping on a natural surface such as napping outside in the grass on a perfect-weather day, we naturally shift positions during sleep. Walking is one of the most dynamic and natural positions for us, and many people can actually walk at a slow pace longer than they can sit up straight. Even when they can't walk any more, it's usually because of foot pain due to our modern footwear and modern surfaces rather than due to back pain.
This is all because sitting up straight is a relatively static position, even if your top half is swaying back and forth, your legs may not be, etc. The ideal computer position is one which puts you in a dynamic state without causing you to be unbalanced. Consider a large inflated air ball as a chair for example, while it seems these might be good for the back by making you sit up straight all of the time, they are really confining your waist to very limited movement, and same for upper thighs, which is where most of the strain is being put due to no back support or movement.
While not as good as walking, the ideal position to be in while working on a computer isn't standing either, because even standing is not enough movement. Even walking in a fixed direction on a treadmill desk is not ideal, because of several subtle reasons (the walking speed of treadmills is fixed and unnatural, manual treadmills are too effort-intense, automatic treadmills also are very confined which is not true natural walking movements, and also the flat surface is bad) and starting and stopping the treadmill every 10 seconds or so is not practical. Therefore, the ideal computer posture/chair, is a rocking chair which has all hard surfaces, like this one:
NOTE: this is not the one I use, I have never used it, and don't recommend it, it is just an image to give you an idea.
The rocking mechanism allows you to easily shift your weight and release pressure on static buildup points on your body. This can be instantaneously started/stopped by rocking with no conscious effort and so it is practical. The hard surface is necessary because it allows your body to be aware of the surface and therefore erect properly (as opposed to a cushion) as well as not constricting around the thighs/waist restricting movement, like a cushion does. When rocking on a slick hard surface, you actually move slightly back and forth in the seat naturally, which is good.
Another thing to keep in mind is that the rocking motion isn't actually the goal, the idea is to lean forward and hold that position as is natural when you use the mouse or keyboard, lean back when reading a line of text, move forward a little just to subconsciously adjust, all spread out over seconds or even minutes. It's not supposed to be an exercise - the purpose of the rocking range of motion is to allow you to shift your center of gravity off of the set of bones and muscles which are stressed due to prolonged static pressure.
Note: Rocking chairs such as the one in the picture are also not confined to one range of movement, as it's also easy to move side to side in them, especially when leaning forward, generally though, the higher the arc of the rocker legs, the easier the movement. If you have very thick carpets or some floor material which prevents sliding of wooden rocker chair legs from turning side to side, consider getting a hard but slick computer floor mat placed underneath it.