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The top row is a series of plots using the escape time algorithm for 10000, 1000 and 100 maximum iterations per pixel respectively. The bottom row uses the same maximum iteration values but utilizes the histogram coloring method. Notice how little the coloring changes per different maximum iteration counts for the histogram coloring method plots.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
This quality of unpredictability and apparent randomness led the logistic map equation to be used as a pseudo-random number generator in early computers. [ 4 ] At r = 2, the function r x ( 1 − x ) {\displaystyle rx(1-x)} intersects y = x {\displaystyle y=x} precisely at the maximum point, so convergence to the equilibrium point is on the ...
The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.
This procedure later became known as a Lorenz map (not to be confused with a Poincaré plot, which plots the intersections of a trajectory with a prescribed surface). The resulting plot has a shape very similar to the tent map. Lorenz also found that when the maximum z value is above a certain cut-off, the system will switch to the next lobe ...
The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.
Time series of the Tent map for the parameter m = 2.0 which shows numerical error: "the plot of time series (plot of x variable with respect to number of iterations) stops fluctuating and no values are observed after n = 50". Parameter m = 2.0, initial point is random.
It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .