If you have an Java enabled browser you will see below generation 2 (or another, depending
on the parameter set in the HTML source) of the plane filling Peano curve.
Clicking on next, you see the next generation
appearing. After 11 clicks it is fully visible and the parent generation has disappeared. Then,
at the next step, the scale is enlarged
by a factor nine showing that the new generation is (self)similar to its parent
Space filling or plane filling
This Peano curve is called a plane-filling curve,
because a square of given size will be filled ever denser by successive generations of this Peano curve.
More mathematically: Given an arbitrairy point in the square and an epsilon > 0, no matter how small,
there will be an N such that the Nth generation Peano curve passes by the given point at a distance
smaller than epsilon.
For an faster way of jumping through different generations of the Peano curve look at this
alternative page which gives some more insight in the construction of this