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The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989. [1] ... or by the following polar equation:
In the mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices and 6 edges. [ 1 ] [ 2 ] It can be constructed by joining 2 copies of the cycle graph C 3 with a common vertex and is therefore isomorphic to the friendship graph F 2 .
A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz.
In mathematics, the algebraic butterfly curve is a plane algebraic curve of degree six, given by the equation x 6 + y 6 = x 2 . {\displaystyle x^{6}+y^{6}=x^{2}.} The butterfly curve has a single singularity with delta invariant three, which means it is a curve of genus seven.
If one draws the data-flow diagram for this pair of operations, the (x 0, x 1) to (y 0, y 1) lines cross and resemble the wings of a butterfly, hence the name (see also the illustration at right). A decimation-in-time radix-2 FFT breaks a length-N DFT into two length-N/2 DFTs followed by a combining stage consisting of many butterfly operations.
To see how this number arises, consider the real one-parameter map =.Here a is the bifurcation parameter, x is the variable. The values of a for which the period doubles (e.g. the largest value for a with no period-2 orbit, or the largest a with no period-4 orbit), are a 1, a 2 etc.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula: [1] = + = + = ().
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...