How does the title A Portrait of the Artist As a Young Man relate to Stephen Dedalus' evolution?

The title of James Joyce's novel, A Portrait of the Artist as a Young Man, refers to it's main protagonist, Stephen Dedalus. The novel follows Stephen throughout his childhood and adolescence, chronicling his life as a toddler, a schoolboy, and, finally, as a young artist setting off into the world to pursue his art. In the title, the words "artist" and "portrait" refer to Stephen's identity as an artist; though Stephen is an aspiring writer, the word "portrait" illustrates his love of art and his ambition to create representations of reality. Furthermore, the final words, "young man," allude to Stephen's youth, inexperience, and growing pains. All in all, the title has come to signify one of the greatest coming of age stories in English literature.

It must be noted that the word "portrait" is a deliberately strange choice here, and so it warrants further inspection. A portrait is a static object, something that neither moves nor evolves over the passage of time. This is a strange word, therefore, to choose as the title of a novel. One can speculate, however, that by using the word "portrait," he meant to add a static form to his novel and to the development and evolution of Stephen himself. Rather than following the easy chronology of earlier works, Joyce was set on creating something truly experimental, a work of literature based on a series of vignettes rather than a traditional narrative. Thus, "portrait" signifies the novel's nearly cubist aesthetic, as it accurately describes the way in which Joyce stitches together scenes from Stephen's life and growth without actually forcing a definite meaning or narrative upon them. 

How does A Portrait of the Artist as a Young Man depict the development of an artist?

A Portrait of the Artist as a Young Man by James Joyce is chiefly concerned with describing the development of Stephen Dedalus not only as a young man, but also as a writer and an artist. In many ways, the narrative is a quintessential example of the bildungsoman, a story that tells of the growth and maturation of a character and that often functions as a coming-of-age tale. In addition to describing his family life and his spiritual development, the narrative focuses on Stephen's growing consciousness as a writer, chronicling his formation of an artistic philosophy and aesthetic.

Additionally (and more importantly) the narrative style mirrors Stephen's development. When Stephen is a young child, the narrative is written to resemble the thought processes of a child. Later on, when Stephen is a mature intellectual attending college, the writing style has also matured to reflect this change. Thus, the artistic style of the novel parallels (and, by extension, illustrates) Stephen's development as an artist. In this way, Joyce gives us a radical account of the conditions for artistic development, and the novel remains an example of innovation despite its age (having been published in 1916, Portrait recently turned 100).