The so-called Chaos Symbol has so much symmetry and order that it's difficult to understand the reason for its choice. Indeed, there are many things about chaos that are difficult to understand; and perhaps the most difficult is understanding why anybody would want to study the subject in the first place.
Even so, some people make their careers from the headache-inducing chaos theory of mathematics and dodgy conclusions based on polynomial computations. But on this page, we restrict our study to just looking briefly at a symbol used by fans of the occultists known as the Illuminates of Thanateros (IOT) who dabble in chaos magic.
For the superstitious, Thanatos was the old Greek personification of death, son of night and darkness. By contrast, Eros was the mythical god of beauty and love-making. One might conclude from the IOT's name that their members love death, and yet they do love life more, generally doing nothing to hasten their own deaths.
Interestingly, although the society dates from only the 1970s, the emblem is based on two much older symbols, the Baptismal Cross and the Barbee Cross, together being symbols not of death, but of immortality.
Like the Christian Church which uses those two crosses, the organisation ('Pact') of the IOT can be quite chaotic at times, where members have squabbled over what this fraternal society's non-chaotic dogma should be. One thing is agreed upon, however, and that is the maintenance of secrecy. Therefore if we knew what their symbol meant to the members, then we couldn't tell you here.
This is the antithesis to the meaning of the symbols used by the Christian Church. Christians may disagree on the interpretation, but they will always be forthcoming of what the cross means to them.