In mathematics, a fractal sequence is one that contains itself as a proper subsequence. An example is 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2...

Sequence". math.bu.edu. Retrieved 17 February 2024. "fibomandel angle 0.51". Desmos. Retrieved 17 February 2024. Lisle, Jason (1 July 2021). Fractals:...

In mathematics, Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in...

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding...

The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(z) ∈ C {\displaystyle...

creating a fractal, using a polygon and an initial point selected at random inside it. The fractal is created by iteratively creating a sequence of points...

four bold numbers in the sequence 1, 5, 10, 10, 5, 1). Gould's sequence is also a fractal sequence. The nth value in the sequence (starting from n = 0) gives...

Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known...

as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve...

Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both...

Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying...

According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension...

Julia set of f {\displaystyle f} , which forms a fractal pattern, sometimes called a "Collatz fractal". There are many other ways to define a complex interpolating...

Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics...

In mathematics, the Rauzy fractal is a fractal set associated with the Tribonacci substitution s ( 1 ) = 12 ,   s ( 2 ) = 13 ,   s ( 3 ) = 1 . {\displaystyle...

triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal with the overall shape of an equilateral triangle, subdivided recursively...

In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing...

The Fibonacci word fractal is a fractal curve defined on the plane from the Fibonacci word. This curve is built iteratively by applying the Odd–Even Drawing...

Fractals "Julia set", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Weisstein, Eric W. "Julia Set". MathWorld. Bourke, Paul. "Julia set fractal...

turns out that the sequence of lengths L {\displaystyle {\mathcal {L}}} of the set itself is "intrinsic," in the sense that the fractal string L {\displaystyle...

A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. The...

In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation f n = f n − 1 ± f...

Koch curve, a fractal curve of infinite length containing a finite area. This illustrates the fractal nature of the Thue–Morse Sequence. It is also possible...

nature are often chaotic, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks...

forward and three waves of correction, the sequence is repeated on a larger degree and the self-similar fractal geometry continues to unfold. The completed...

cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional...

interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of...

method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were...

A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by...

fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal...