What is the theoretical dimension of a fractal?
The theoretical fractal dimension for this fractal is 5/3 ≈ 1.67; its empirical fractal dimension from box counting analysis is ±1% using fractal analysis software. A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale.
How to see the shape of a fractal machine?
The shape you see is the combined output of the controls below. Mouse over them to see what they do. If the page gets too slow, turn some of the parameters down. Press H or ~ to hide the controls. Find out more in this blog post. This slider changes the first and last angles of the motif.
What is the history of the fractal form?
The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal forms along the way.
Where are fractals found in the natural world?
One of the things that attracted me to fractals is their ubiquity in nature. The laws that govern the creation of fractals seem to be found throughout the natural world. Pineapples grow according to fractal laws and ice crystals form in fractal shapes, the same ones that show up in river deltas and the veins of your body.
Is there a fractal dimension calculator for Mac?
FDC is a Mac OSX application that can be freely downloaded for evaluation. It is fully functional except that offset sampling (a critical feature for good estimates of the fractal dimension) isn’t enabled.
Which is the fractal dimension for South Africa?
log[L(s)] = (1-D)log(s) + bwhere D is the Fractal Dimension. For Great Britain, 1 – D = -.24, approximately. D = 1-(-.24) = 1.24, a fractional value.The coastline of South Africa is very smooth, virtually an arc of a circle. The slope estimated above is very near zero. D = 1-0 = 1.
How many fractals have the same Hausdorff dimension?
The boundary and the set itself have the same Hausdorff dimension. For determined values of c (including c belonging to the boundary of the Mandelbrot set), the Julia set has a dimension of 2. Every Peano curve filling the plane has a Hausdorff dimension of 2. And a family of curves built in a similar way, such as the Wunderlich curves .