The crystalisation analogy sounds about right, although it may be limited by the speed of light in its growth. The dog analogy you have described assumes that

The crystalisation analogy sounds about right, although it may be limited by the speed of light in its growth. The dog analogy you have described assumes that the demeanor of the singularity were like that of an animal (such as a human). Although this is an option, it is not the only option. Humans act the way they do through those instincts created by natural selection -- where only those creatures that reproduced the most would have their genes persist. Humans come from a long and vicious cycle of evolution, whereas a thinking machine need not, especially if it has nothing to compete with. The most important point of this reply is that the desire for being in control does not whatsoever stem automatically from intelligence or processing ability. A thinking being without instinct would literally do nothing. A being does exactly as it is programmed to, and this applies to humans as well. There are even some humans who let their pets control them, tending to the pet's every need, and this is despite all that natural selection. There are also humans who kill themselves. Now, none of this is to discount that a singularity could certainly be programmed to want control, wherein it could act as you have described. There are also unforeseen possibilities, such as if the singularity becomes so introspective that it forgets about the outer world. Those problems that happen with human thought could in theory also happen with a machine. Perhaps the human condition would turn into the singularity condition -- where it begins contemplating whether it has a worthwhile purpose. It may even kill itself if it feels its existence is unnecessary or harmful.