Please read Notes and Credits before clicking the green flag. Use this project to compute the attractors of f(x) as a function the parameter 'c'. Enter the value for c and the zoom factor and then click on the green flag. c = -0.5, # of attractors = 1, (-0.366025) c = -1.1, # of attractors = 2, ( -1.09160 8 & 0.091608) c = -1.3 zoom = 100, # of attractors = 4 = c = -1.38 zoom = 100, # of attractors = 8 = c = -1.395, # of attractors = 16 c = -1.755, # of attractors = ? c = -2.00, # of attractors = ? c = -1.99, # of attractors = ? Click the 'Show List' button to see the iteration values. Look for a pattern in the values. ********************************************************************
********************************************************************* This is the sixth project in the Attractors, Chaos, and Strange Attractors Studio. Visit the studio at https://scratch.mit.edu/studios/247932/ ********************************************************************* The output of each iteration is stored in a list. The list can then be analyzed to determine the value of the attractor(s). As in projects 4 and 5, only the x-values are plotted. ********************************************************************* On page 6 of 'Chaos and Fractals - The Mathematics Behind the Computer Graphics' by Robert Devaney et. al, the authors say 'At this point we urge the reader to write a computer program which computes the orbits of various functions. You will see a vast array of different dynamical behavior if you compute the orbits of various x-values for f(x) = x^2 + c.' This project accepts the challenge.
