The short answer:
It is not forbidden per se, but not in the spirit of Shabbos.
The Long answer:
There are acts in Hilchos Shabbos that are actually forbidden like striking a match. These are defined as the 39 Melachos and their Toldos.
But one has to ask oneself a pertinent question - why? Why are creative/destructive acts purposefully forbidden?
The old argument is as follows: It is forbidden to strike a match - a seemingly simple act, and moving furniture around your apartment - assuming that's all you're doing - heavy lifting of sofas around - is permitted?
The answer lies in the purpose of Shabbos - closeness to Hashem. The point of Shabbos is to rest and become attuned to the Creator of the Universe.
That is why the 39 Melachos are a framework of forbidden activity - but there are positive actions - making kiddish, having a lavish meal, Singing songs, spending time with family, learning divrei Torah make Shabbos into a spiritually rich experience.
The spirit of Shabbos is just that - connecting with Hashem, so while reading magazines is not an intrinsic problem - assuming that you're just being entertained by them, and not thinking about doing a melacho with the material, then it is not forbidden, but it is not in the spirit of Shabbos.
The derivation of the Melachos of Shabbos comes from the building of the Mishkan (Bava Kama 2a). That is all the forbidden actions were performed in building or doing something in the Mishkan. The Mishkan is a microcosm of Hashem's creative energy in a spatial manner in this world. We're severely lacking in our regard of this, because we don't have a Beis Hamikdash - but the idea is that the Mishkan is supposed to be spiritually infusing us with kedusha and holiness and the recognition that G-d really loves us and wants to be close. In that sense we have Shabbos to re-connect with G-d, by not doing these creative acts, we're expressing G-d's will and presence in this world. So Shabbos is about creating that space of holiness every week.
Everyone has an interest. Perhaps it might be helpful to get hold of "The Midrash Says" and read that specifically on Shabbos - the stories should be of entertaining value, give insights into the Parsha, and you'll learn something and create an atmosphere of holiness as a substitute to the magazines.