Gosper Island is a base-motif fractal formed by using the
following base and motif: Performing generator iteration, we
substitute every side of the hexagon with the motif: We then
again substitute every line segment with the motif and continue
the iteration: In addition to the side of this figure being
self-similar, the Gosper Island itself can be broken down into 7
small versions of itself: Similarly to the Koch Snowflake, which
can be filled by Snowflake Sweeps, the Gosper Island can also be
filled by a fractal like this: The fractal dimension of Gosper
Island can be easily found using the similarity method. The
motif of the fractal is composed of 3 identical line segments,
each of which is 1/sqr(7) long. The fractal dimension is thus
log 3 / log (sqr(7)), which is approximately 1.129. With every
iteration, the length of this curve becomes 3/sqr(7) times
longer. After an infinite number of iterations, the curve, just
like all fractal curves will become infinitely long. If you
substitute a line segment with