Successive Golden Rectangles dividing a Golden
Rectangle into squares (logarithmic spiral known as the golden spiral)
The Statue of Liberty
The Statue of Liberty was presented to the United States by the people of France in 1886. Standing on Liberty Island in New York Harbor, it welcomes visitors, immigrants, and returning Americans. The copper-clad statue, dedicated on October 28, 1886, commemorates the centennial of the signing of the United States Declaration of Independence and is a gesture of friendship from France to the United States. Frédéric Auguste Bartholdi sculpted the statue and obtained a U.S. patent for its structure. Alexandre Gustave Eiffel (designer of the Eiffel Tower) engineered the internal structure. Eugène Viollet-le-Duc was responsible for the choice of copper in the statue's construction and adoption of the repoussé technique, where a malleable metal is hammered on the reverse side.
A golden rectangle
is a rectangle whose side lengths are in the golden ratio,
one-to-phi, that is, approximately 1:1.618. A distinctive
feature of this shape is that when a square section is
removed, the remainder is another golden rectangle, that is,
with the same proportions as the first. Square removal can
be repeated infinitely, which leads to an approximation of
the golden or Fibonacci spiral.
The Droste effect is a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration geometrically reduces the picture's size. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry.