Symmetry and chaos: the shape of snowflakes.

To respond briefly to the question that gives the title to his book, yet I quote Ian Stewart:

Equations in itself devoid of any symmetry sometimes give rise to a regular dynamic and sometimes to chaos. It was discovered that this is true even for the symmetrical equations. If you change the numeric coefficients of the equations, one can obtain a chaotic dynamic that obeys to symmetrical rules. A symmetrical chaos. What are the systems of this kind? The simplest answer you get from thinking of the geometric representation and the attractors. What we discover is that the attractors are chaotic (because dynamics are chaotic) and symmetrical (because rules are symmetrical).

Ian Stewart - What shape is a snowflake? (translated from Italian).