Morphology is "the study of the form of things", and morphogenesis (in biology) is "the origin and development of morphological characteristics, according to Oxford Dictionaries .
Christopher Alexander speaks to morphogenesis in the context of built environments, drawing inspiration from biology.
Things in the biological world, almost by definition, are created continuously by morphogenesis, that is by a process which is all the time growing and adapting, whether it be in a growing embryo or in a forest or a field, and which gives form, progressively, while growth and change and adaptation are happening. In real morphogenesis the form of what is coming, or what is about to be, is always drawn from the form of what was in the moment just before. That is, things are always going like that. If a tree is growing for 500 years, it is continuously unfolding from its previous state, and then what we see and recognize is first of all in itself a process. But even if you just look at it in its static state, it is at that moment the end product of transformations that have been going on, and on, and on. And these are the things which give it shape, form, and substance. Traditional society also managed to do something very much like that – that is to say, morphogenesis -- with buildings, plazas, streets, fences, windows and so forth. And I shall show many examples of this phenomenon. But the point is that up until somewhere around a hundred years ago -- until it started to get off the tracks -- a human-inspired version of this natural morphogenesis, was going on whenever something was built. This was true of fields, forests, churches, houses, streets, even a window or a bench. Whatever it was, it was shaped, modified, shaped again, and adjusted and so on, and so on, and so forth. As a result of the morphogenesis and the complex adaptation that was possible under these conditions, the places people made had life.
Christopher Alexander. 2004. “Sustainability And Morphogenesis: The Birth of a Living World”. presented at the Schumacher Lecture, Bristol, UK, October 30. http://www.livingneighborhoods.org/ht-0/archive.htm

In real morphogenesis the form of what is coming, or what is about to be, is always drawn from the form of what was in the moment just before. That is, things are always going like that. If a tree is growing for 500 years, it is continuously unfolding from its previous state, and then what we see and recognize is first of all in itself a process. But even if you just look at it in its static state, it is at that moment the end product of transformations that have been going on, and on, and on. And these are the things which give it shape, form, and substance.