Search Results for ""

The Pythagoras tree is a fractal constructed iteratively from a right triangle with squares erected on each of the sides. Subsequent iterations add additional similar right ...

A polygon that can be dissected into n smaller copies of itself is called a rep-n-tile. The triangular polygonal spiral is also a rep-tile. The above figure shows the zeroth ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

The fractal J(-3/4,0), where J is the Julia set. It slightly resembles the Mandelbrot set.

An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

The hyperbolic sine integral, often called the "Shi function" for short, is defined by Shi(z)=int_0^z(sinht)/tdt. (1) The function is implemented in the Wolfram Language as ...

A Julia set with c=-0.390541-0.586788i. The fractal somewhat resembles the better known Mandelbrot set.

A fractal which can be written as a Lindenmayer system with initial string "YF", string rewriting rules "X" -> "YF+XF+Y", "Y" -> "XF-YF-X", and angle 60 degrees.

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

A piecewise linear, one-dimensional map on the interval [0,1] exhibiting chaotic dynamics and given by x_(n+1)=mu(1-2|x_n-1/2|). (1) The first few iterations of (1) give x_1 ...