Why is spiral antenna frequency-independent?

I have read Stutzman's "antenna theory and design" about this question.In the book the explanation is that spiral antenna is self-complementary but I just don't comprehend how self-complementary does for frequency characteristic.

The real reason is that it is logarithmic angled.

Hi ermai,

You meant to say "self-similar" rather than "self-complementary", right?
Properties of an antenna with respect to frequency are related with the ratio of their dimensions with wavelength. For example, If you have a given antenna (e.g. a dipole) with some properties at frequency f_o and you double all its dimensions, the new antenna has that same properties (radiation diagram, impedance, etc) at frequency f_o/2. The same apply for any scaling factor, than in the exaple is 2.
An infinite logarithmic spiral is a line that has the property that scaling it by any factor gives itself. The same property have, for example, an infinite biconical antenna or an infinite straight wire.
Self-similarity not necessarily implies that the antenna is a good radiator. It just means that its properties are the same an all frequencies.
Self-similar lines, figures or bodies are necessarily infinite. Practical antennas are of course finite (both the "big part" and the "small part" of a spiral is cut). So, self-similar practical antennas are frequency-independent only in some finite bandwidth.
Regards

Z