In most people the left and right brains work together to create a recognizably human being. This wondrous dance is going on all the time, and the two hemispheres are always communicating with one another, but the communication isn't symmetrical.
The right brain is connected to the world, monitoring all the senses all the time we are awake. When the eyes are open, the right brain takes in a huge amount of information, including all the peripheral vision. Each eye has well over 100 million photoreceptors, the vast majority of them rods, which are very sensitive to light. The right brain pays attention to all of them and reacts when enough of them change in various patterns. The reaction often includes directing the eyes to turn toward the change and directing the left brain's attention to it.
The sense change might come from sound in the ears or a touch on the skin. Whether the change comes from those or vision, the right brain often directs the eyes to the perceived 3D location (which only the right brain knows) and tells the left brain to focus its attention and 2D vision on that sight.
Typically, the left brains drops whatever it was doing and places its attention on the center of vision (right center visual field only). It takes apart the visual field in a multistep process. First, the left visual cortex decomposes the 2D image into its component parts. Next, the decomposed visual field is passed through the various filters mentioned in the previous post to come up with an understanding or explanation or possibility of what created the change. Note that this change in attention is at the expense of whatever was being attended to previously.
Meanwhile, the right brain continues to pay attention to the changed area using the entire visual field. The right brain looks for threats to survival. Some threats may be built into our genes: there's some evidence that snakes and spiders may fall into this category and that relatively simple pattern recognition can invoke this response. Other threats are the result of learning from previous encounters. Such learning can be embodied in right-brain pattern recognition that responds quickly by directing the body to flee or otherwise react. A reaction that can be mediated only by the right brain reaction will happen very quickly, in most cases quickly enough to be successful.
Meanwhile the left brain will be decomposing the event both spatially and temporally. This takes time, so the threat better not be imminent if the left brain is involved. On the other hand, if it's a new threat, the right brain may not recognize it, so the slow, klunky analysis performed in parallel by the left brain may be the only thing that saves you. And if you survive the encounter, the analysis by the left brain can be returned to the right brain as a lesson that will allow faster response in the future.
The interaction of the left and right brains was just now described in terms of threats, but the same description can be made for opportunities. Suppose you are hungry. Walking through the jungle or savannah, your right brain takes everything in and finds all the normal sources of food very quickly. But what if there are no normal sources? A sufficiently starving right brain will notice anomalies in the environment that don't reach the threshold for food sources and direct the left brain to consider them. The left brain might deconstruct the anomaly and come up with a plan to turn it into food while the right brain continues to scan for known food and threats.
Thus the normal integrated operation of the two brains is for the right brain to direct the attention of the left brain to sensory anomalies while continuing to connect to the world, for the left brain to discover new aspects of the world based on those anomalies and return the new information to the right brain, and for the right brain to integrate the new information from the left brain into its larger world view for long term advantage. I call this the right-left-right paradigm. This process happens continually in healthy human beings, and this the process that has allowed our species to advance so radically for tens of thousands of years.