They're altogether compound, the Aster Family

Behold, a giant sunflower, the best-known and most beautiful member of the Asteraceae, or aster family.  The Asteraceae is a huge family with many important members, and it is considered one of the most complex and highly specialized plant families.  The structure of aster-type plants is very different than the basic plant structure, which means it has changed a lot from its evolutionary ancestors.  The Orchid family (Orchidaceae) is also considered highly specialized, and it is an equally large and important plant family. 

Sunflower

The sunflower variety seen here has been bred to produce amazing quantities of  sunflower seeds, but it will serve as my example for how this plant family works.  All members of the Asteraceae have flower heads that are actually clumps of tiny flowers.  If you look closely at the sunflower head above, you will see that is is composed of hundred of tiny yellow and brown structures.  Each of these is a separate flower with its own miniature petals and male and female reproductive structures.  The main flowers in the sunflower are disk-type flowers.  These disk flowers are found in the center of Asteraceae flower heads.  When you look closely at the petals at the edge of the sunflower head, you can follow each one in to see that it is the single petal for a small flower on the edge of the sunflower head.  Flowers with a single large petal are called ray flowers.  Next time you encounter an aster-type flower, tear it apart to observe how it's put together.  You'll easily see how the miniature flowers are clumped together.

Some members of the Asteraceae have only ray flowers, like dandelions and chicory.  Others have only disk flowers, like thistle and ageratum.  Most composits, as members of the Asteraceae are also called, have both disk and ray flowers, like daisies, rudbeckias and zinnias.  Often ray flowers are infertile, meaning they don't actually produce seeds.  On the sunflower above, the disk flowers will each mature into sunflower seeds, but the ray flowers will just fall off.  Their job is finished after they have attracted bees to the newly-opened flower head.  Disk flowers are inconspicuous and do not attract bees very well, even though they produce seeds.

In zinnias, the ray flowers mature first, which you can see in the picture below.  You might just call the ray flowers petals, if you didn't already know better.  Disk flowers mature as the flowers age.  They look like yellow mini-flowers in the center of the main flower. 

Zinnia

Below is a row of rudbeckias, also known as Mexican hat flowers.  Rudbeckias, like most aster-type flowers are great at attracting pollinators like bees, butterflies and other insects.  The pollinators they attract also pollinate other plants nearby, like the tomatoes in the next row.  Many of the pollinators are also predatory insects that help to eat harmful insects.  These flowers are an important farm crop, but they also help keep the farm working smoothly and make it look gorgeous.

Rudbeckia

 I couldn't resist including this last picture.  I spent my first hour on the farm today harvesting zinnias and sunflowers, my two favorite flowers.  It was a special delight to walk among the 7-foot-tall sunflowers as they faced the morning sun.  The bees were just getting started working for the day, and their buzzing grew louder by the minute.  By the time I was finishing, I had to wave bees off of the flowers as I cut them down.  They were surprisingly patient with me, just moving on as their flowers fell beneath them.  As I finished the task, I carried away sunflowers by the armful for some very lucky farm customers.

Sunflowers facing the sun