It is a myth that contemporary architecture has abandoned the need for symmetry, and has chosen the asymmetry as a dominant stylistic pattern.
It is true that nowadays you will rarely find a new building whose main façade is perfectly symmetrical on its central vertical axis. In the past, particularly during periods inspired by classicism, this feature was almost compulsory for an architecture having any ambition to monumentality. Why? Probably because the symmetry was considered one of the properties of venustas (harmony or beauty), one of the three pillars of the Vitruvian triad, along with firmitas and utilitas. Temples, churches, palaces almost always have this property, which – in the language of habit – still tells us: “you’re in front of an important building.”
Similarly, a series of arches forms an agorà, four porches a forum, two hemicycles an arena, and so on. Therefore symmetry has to do not only with monumentality, but also with the identification of the building through the sequence of similar parts, whose predictability reassures us about the nature or function of what we see.
Gradually going towards increasingly complex patterns, we meet the rotational symmetry, which allows the formation of central-axis spaces of great formal richness, and the translational symmetry, which allows us to move the axis in space producing interesting “distance references” and “domino” effects of great beauty (i.e. castle towers or city walls).
With medieval architecture, symmetry becomes comparison between parts of the composition different in form but similar in expressive power: any French or German Gothic cathedral, for example, rarely has the two towers of the facade exactly alike; nevertheless, the facade is harmoniously symmetrical in the alternance of full and empty, high-low, projecting-recessing.
Far from simplifying or impoverishing the forms, the properties of symmetry thus constitute a rich and versatile instrument of architectural composition: communicating that “those are the same”, we actually suggest (whether consciously or not) other meanings: “this is more important than that” or “this is the center” or “this is in the composition, this is out.”
Without going too far back in time, let us recall the holy symmetries made by Louis Kahn, or the irreverent ones by Robert Venturi (with the solid element in the center, instead of the caved one) or the ironic compositions by James Stirling.
One can endlessly multiply the game, repeating and combining in different ways the reflections and similarities at different scales; you get to the fractals, shapes resulting from complex mathematical functions, found in biological geometry (cabbages, shells) and in the constructions of primitive cultures . In fractals the same basic form is repeated in different sizes, from the tiny element to the whole structure, such as the domes of Jain temples, the huts and villages Songhai in Mali, the Jewish Museum in Berlin by Daniel Libeskind.
Is there any such thing that may be called asymmetry? Or is it not itself a supercomplex form of symmetry? Or, putting it another way, isn’t any composition made with intellect inherently symmetrical, so that no place remains for asymmetry aside from that of pure chaos?
Maybe it is not up to the architect but to the philosopher to answer these questions. What can be put in the toolbox of the designer? First, the awareness that the richness of forms, from simple to complex, goes far beyond the form itself, and refers in space and time to other places, other meanings, other perceptions; and furthermore the ability to manage these references in a poetic form, to give his work a sense or a quality that it will be the observer’s task to reconstruct or reinvent for his own benefit.
 Ron Eglash, African Fractals. Modern Computing And Indigenous Design (1958) Rutgers University Press, New Brunswick, New Jersey and London.