From your description, it would be my guess from the "swirls and bulls-eyes" you mentioned that your kitty is a classic (blotched) tabby.
For those less familiar with the patterns, here is a bit of data. You never know, these little factoids could be good for those Trivial Pursuit nights at home with pizza and beer. *smile*
In all cats, one of three forms of a tabby pattern gene is always present. The most common is the classic or blotched tabby with broad, swirling markings. The mackeral tabby has narrower stripes. The third form is the ticked (see #3 below) tabby (also called Abyssinian tabby but this form is NOT restricted to the breed that typifies it), which has all-over agouti hairs (see #1 below), the only marking being a suggestion of the "M" mark (known as the Scarab mark in some cats) on the forehead that is common to all tabbies. A fourth form of tabby, the spotted, is thought to be a version of the mackeral form in which the stripes have become broken up. By convention the color of a genetically black tabby is known as brown (from the color of the agouti hairs, not the stripes).
1) Agouti is the fundamental coat pattern of many mammals, including cats, in which each guard hair (see #2 below) has one of more pale yellow bands known as the agouti bands between darker bands of any one of ten or so colors that gives the coat a flecked looking (ticking #3 below); in domestic cats a tabby pattern of unbanded hairs (in the same color as the darker bands in the agouti hairs) is always superimposed on the agouti pattern; removal of the agouti band by the non-agouti gene(#4 below) gives rise to overall solid color (but this gene is ineffectual on red, cream and apricot).
2) Guard Hair - The long, bristle-like hair that makes up the outer layer of the coat. Also referred to as awn hair or incorrectly, some also call it down hair.
3) Ticking - the flecked effect seen in the areas between the markings in tabby coats that is created by the darker bands on the agouti hairs.
4) Non-Agouti -Describes a coat or cat influenced by the non-agouti gene, which effectively converts the basic tabby pattern into an overall solid color (but this gene is ineffectual on red, cream and orange colors).
Hope this helps at least some. There are some real good books that can help you if you have an interest in this kind of stuff. Let me know if you want a "recommended reading list". *smile*
My continued best to you and yours,