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While an optimally packed fractal appears only for a defined value of r, i.e., r opt, it is possible to play the chaos game using other values as well.If r>1 (the point x k+1 jumps at a greater distance than the distance between the point x k and the vertex v), the generated figure extends outside the initial polygon. [5]
von Koch curve with random interval; von Koch curve with random orientation; polymer shapes; diffusion-limited aggregation; Self-avoiding random walk [8] Brownian motion; Lichtenberg figure; Percolation theory; Multiplicative cascade
The Ulam spiral was described in Martin Gardner's March 1964 Mathematical Games column in Scientific American and featured on the front cover of that issue. Some of the photographs of Stein, Ulam, and Wells were reproduced in the column.
Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines , circles or other points.
Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale . Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension ...
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
Built by scaling the 50 segment generator (see inset) by 1/10 for each iteration, and replacing each segment of the previous structure with a scaled copy of the entire generator. The structure shown is made of 4 generator units and is iterated 3 times. The fractal dimension for the theoretical structure is log 50/log 10 = 1.6990.