Search results
Results from the WOW.Com Content Network
Floyd's triangle is a triangular array of natural numbers used in computer science education. It is named after Robert Floyd . It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1 in the top left corner:
The time-space diagram of a replicator pattern in a cellular automaton also often resembles a Sierpiński triangle, such as that of the common replicator in HighLife. [9] The Sierpiński triangle can also be found in the Ulam-Warburton automaton and the Hex-Ulam-Warburton automaton. [10]
The pattern obtained by coloring only the odd numbers in Pascal's triangle closely resembles the fractal known as the Sierpinski triangle. This resemblance becomes increasingly accurate as more rows are considered; in the limit, as the number of rows approaches infinity, the resulting pattern is the Sierpinski triangle, assuming a fixed ...
The pattern derives its name from the fact that it is characterized by a contraction in price range and converging trend lines, thus giving it a triangular shape. [ 1 ] Triangle patterns can be broken down into three categories: the ascending triangle, the descending triangle, and the symmetrical triangle.
Klauber's 1932 paper describes a triangle in which row n contains the numbers (n − 1) 2 + 1 through n 2. As in the Ulam spiral, quadratic polynomials generate numbers that lie in straight lines. Vertical lines correspond to numbers of the form k 2 − k + M. Vertical and diagonal lines with a high density of prime numbers are evident in the ...
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
In the spiral, each triangle shares a side with two others giving a visual proof that the Padovan sequence also satisfies the recurrence relation = + ()Starting from this, the defining recurrence and other recurrences as they are discovered, one can create an infinite number of further recurrences by repeatedly replacing () by () + ()
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.