Ads
related to: fractal math examples worksheets
Search results
Results from the WOW.Com Content Network
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set .
Each branch carries 3 branches (here 90° and 60°). The fractal dimension of the entire tree is the fractal dimension of the terminal branches. NB: the 2-branches tree has a fractal dimension of only 1. 1.5850: Sierpinski triangle: Also the limiting shape of Pascal's triangle modulo 2.
The first few steps starting, for example, from a square also tend towards a Sierpiński triangle. Michael Barnsley used an image of a fish to illustrate this in his paper "V-variable fractals and superfractals." [2] [3] Iterating from a square. The actual fractal is what would be obtained after an infinite number of iterations.
In this approach, pixels that are sufficiently close to M are drawn using a different color. This creates drawings where the thin "filaments" of the Mandelbrot set can be easily seen. This technique is used to good effect in the B&W images of Mandelbrot sets in the books "The Beauty of Fractals [9]" and "The Science of Fractal Images". [10]
So, for example, any point of the circle is a local cut point. In the same paper Whyburn gave another characterization of the Sierpiński carpet. Recall that a continuum is a nonempty connected compact metric space. Suppose X is a continuum embedded in the plane.
Fractal fern in four states of construction. Highlighted triangles show how the half of one leaflet is transformed to half of one whole leaf or frond.. Though Barnsley's fern could in theory be plotted by hand with a pen and graph paper, the number of iterations necessary runs into the tens of thousands, which makes use of a computer practically mandatory.
Ads
related to: fractal math examples worksheets