Mandelbrot Set

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Mandelbrot SetAlexis Ventura11/8/2023. Fall 2023.George Mason University 401: Mathematics Through 3D Printing.The focus for this print is the Mandelbrot set. The Mandelbrot set is a set that is generated by iterations of a function on the complex plane x + i*y. The quadratic polynomial used for the iterations is of the form f(x) = x^2 + c, where c is a constant number of the set. To initiate the iterations, there is an x_0 applied to the function x_1 = (x_0) ^2 + c to get the first computation of x_1. Then we take the previous computation and apply it to the next and then the next signifying an iteration of the function x^2 + c. The more you iterate the quadratic polynomial, the model of the Mandelbrot will get bigger and bigger.For my printed object, I did it on the Mandelbrot set model where I iterated the function of f(x)=x^2+c to max of 50 as according to the following code: MandelbrotSetPlot[{-0.41+0.59I,-0.33+0.69I},MaxIterations→50]. Then I did several data commands to display different types of models of the Mandelbrot set. On the final data command to export to a stl file, I decided to go for a Maximum iteration of 15 as the iteration would provide a good image model of the Mandelbrot set. My Mandelbrot set object was printed on a Creality Ender-3 Pro 3-D printer and the 3-D object took about three and a half hours to print. It is scaled at 106 in width and length to print a decent model of the Mandelbrot set object. It does not use any support, uses brim as the build-plate adhesion, the infill density was at 70% using grid pattern, and the printing temperature was at 215 degrees. This one was the first print and it came out with satisfactory. Devaney, Robert. Unveiling the Mandelbrot set. University of Cambridge, 2006.