Lsystem Construction
If using a Lindenmayer system then the construction of the C curve starts with a straight line. An isosceles triangle with angles of 45°, 90° and 45° is built using this line as its hypotenuse. The original line is then replaced by the other two sides of this triangle.
At the second stage, the two new lines each form the base for another rightangled isosceles triangle, and are replaced by the other two sides of their respective triangle. So, after two stages, the curve takes the appearance of three sides of a rectangle with the same length as the original line, but only half as wide.
At each subsequent stage, each straight line segment in the curve is replaced by the other two sides of a rightangled isosceles triangle built on it. After n stages the curve consists of 2n line segments, each of which is smaller than the original line by a factor of 2n/2.
This Lsystem can be described as follows:


Variables: F Constants: + − Start: F Rules: F → +F−−F+

where "F" means "draw forward", "+" means "turn clockwise 45°", and "−" means "turn anticlockwise 45°".
The fractal curve that is the limit of this "infinite" process is the Lévy C curve. It takes its name from its resemblance to a highly ornamented version of the letter "C". The curve resembles the finer details of the Pythagoras tree.
The Hausdorff dimension of the C curve equals 2 (it contains open sets), whereas the boundary has dimension about 1.9340 .
Read more about this topic: Lévy C Curve
Other articles related to "construction":
... introduced at each stage are each shorter than the lines that they replace, so the construction process tends towards a limit curve ...
Famous quotes containing the word construction:
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)