An attractor is a very complex geometric object.
In fact it is an object of infinite complexity!
You can understand in some way where this complexity
comes from,considering for example that when you
feed back in the formula the previous value, you are
considering a new formula, obtained by replacing
x and y with the previous formula.
The new formula is more complex and if you repeat this
for a few times you get an impossibly long formula!
Another way to represent it is by considering
that your formula like the hands of a baker manipulating
a dough,is transforming all the points in the plane,
rotating,scaling and translating them at each iteration.
The second time it acts on the result of the previous
manipulation, getting a new more twisted "dough".
After a few iterations what you obtain is an object
of great complexity.