Tree diagrams as an aid to reasoning and to illustrate complex relationships have been in use for a period approaching two millennia. The family tree is perhaps the best known historic example, but tree diagrams have always had a much wider range of uses. Today's most familiar use is in the "file tree" that graphically represents the folder structure of personal computer operating systems. Mentally, the tree concept also underlies the document object model (DOM) used in web documents, where elements are viewed as a family with "parents" and "children" and where programs that search for elements by following this logical structure are said to "walk the DOM tree".

A survey of the history of tree diagrams is a humbling experience, since one grasps that the earliest users of the diagram had a broad vision of the invention, and never perceived its modern name, the "tree", as more than a metaphor. While trees in nature can only grow upwards from the soil, there has never been any "natural" position on the page for the root of a branching diagram: it may be at the left, right, top, bottom, or even at the centre in the case of the radial "tree".

While trees in nature must be entirely connected by their wood, the lines of connection in a tree diagram are optional: white space and an axial arrangement are generally sufficient to show the relationships on a page or screen, and joining lines can often be dispensed with.

A certain artistic humour is evident in paintings down the century that have played with the notion that a tree diagram has some affinity with trees in nature. There have been countless ironic observations from artists suggesting that the tips of the tree diagram are indeed like leaves of a tree, or that the roots are immersed in dirt and that nuisances may lurk in the boughs. Our ancestors would have doubtless smiled and moved on, but children often misinterpret humour and metaphors, and construct their own worlds based on misunderstandings.

That is perhaps the origin of a great deal of sterile experimentation with ways to make branching diagrams look more tree-like, usually at the expense of both convenience and clarity.

Generations of genealogists have been obsessed with drawing family trees to somehow resemble nature's trees, and have wasted endless effort trying to fit that vision into printed books, onto typewritten pages and even onto computer screens. Genealogy computer programs usually offer a variety of tree representations to accommodate the preconceptions of their users about how a tree ought to look. When I drew my first family tree with a text-processing program in about 1985, I too spent an inordinate amount of time devising ways to "flow" the tree vertically, neatly connecting the nodes by vertical lines constructed from the pipe symbol in a golf-ball printer's character set and assembling horizontal lines out of underline symbols.

Most people drawing trees do not insist that the root always be at the bottom. They find the inverted tree, with its root at the top, equally satisfying, but are very determined to represent "ascent" and "descent" in a genealogy chart, or "higher" and "lower" in a hierarchy chart, with the up and down axes of the page.

A greater willingness to use trees which grow from a root at the top left corner of the page has probably come about through familiarity since about 1990 with file trees on the Microsoft Windows computer operating system. Windows, in its iterations up to Windows XP, portrayed the "desktop" as the root. To the right and below it, the stored folders and files were depicted in a branching structure. Such "sideways trees" have in fact been common since the birth of moveable-type printing.

In reviewing the development of this type of figure, I shall speak of "branch diagrams" or “stemmata” rather than trees, since it is plain that the "tree" metaphor was only a loose term for this type of figure in the early medieval period, and that these figures had other names in antiquity and in non-western cultures. The term "tree" is no longer an all-embracing one. Today's branching diagrams are drawn in less treelike ways, while the names of figures such as "mind maps" or "rationale maps" dispense with the word "tree" altogether.

We will discuss the various graphic ways of representing hierarchies on a page, but will not be concerned with embellishments of that idea in art, and will only discuss non-graphic notations inspired by the stemma, such as d'Aboville numbers, to the extent that these notations employ their own macro-typography conventions when they must be set up in print.

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