Composite Flowers - Orange Coneflower

I did not know that a Composite flower is actually a composite of many smaller flowers. And - on reading this, I still did not get its meaning. An example is a Sunflower, and so I zoomed in on an image I have of a sunflower - I did not see anything that fit this description! I like this discussion, taken in entirety from this reference: wildflowers-and-weeds.com: Asteraceae

The uniqueness of the Aster or Sunflower family is that what first seems to be a single large flower is actually a composite of many smaller flowers. Look closely at a sunflower in bloom, and you can see that there are hundreds of little flowers growing on a disk, each producing just one seed. Each "disk flower" has 5 tiny petals fused together, plus 5 stamens fused around a pistil with antennae-like stigmas. Look closely at the big "petals" that ring the outside of the flower head, and you will see that each petal is also a flower, called a "ray flower," with it's petals fused together and hanging to one side. Plants of the Aster family will have either disk flowers, ray flowers, or both. When the seeds are ripe and fall away, you are left with a pitted disk that looks strikingly like a little garden plot where all the tiny flowers were planted.