NEWTONIAN FRACTAL SWEETNESS /--/ /--/ /------/ /--/ /-------\ | | | | | ____| | | | __ \ | |__| | | |___ | | | | | | | | | | | | | |__| | | __ | | __| | | | / | | | | | |___ | |___ | -----/ | | | | | | | | | | /--/ /--/ /------/ /------/ /--/ ---------------------------------------------------------------------------------------- Function: ---------------------------------------------------------------------------------------- This fractal generator only accepts polynomials with one variable, specifically 'z'. If you enter a variable other than z, an error window will pop up letting you know that your function won't work. For multiplication write '*' instead of 'x', and be sure to put an asterisk between a variable and a scalar coefficient. For example the function 'x^3-2x+5' will not run, but changing it to 'x^3-2*x+5' will work correctly. ---------------------------------------------------------------------------------------- General Settings: ---------------------------------------------------------------------------------------- These settings affect both "Color Display" and "Gradient Display". Specifically they tell the program how to determine whether or not each point converges to zero, which points to test for convergence, and how many points will be tested. Resolution: This setting determines the resolution of the fractal you are generating. For example, typing in '100' will generate a 100 by 100 grid of points to be drawn. The maximum resolution of the displayed image is approximately 500, anything greater than this will improve the image little, if at all. Higher resolution increases processing time substantially. Iterations: This is the number of times the program runs the newtonian algorithm for finding a zero. More iterations means a higher chance of finding a zero (in other words, each point has a higher chance of converging.) Increasing the number of iterations increases processing time substantially. xmin/xmax: These two settings determine the x-axis span of the initial matrix which is used to produce the fractal. The x-axis represents the real potion of the complex numbers. ymin/ymax: These two settings determine the y-axis span of the initial matrix which is used to produce the fractal. The y-axis represents the imaginary part of the complex numbers. ---------------------------------------------------------------------------------------- Color Display: ---------------------------------------------------------------------------------------- These settings tells the program how to determine convergence for a color image after the zeros have been calculated. Tolerance: The tolerance lets the program know how close each point must be to a zero in order to be considered "converged". A smaller tolerance equates to less convergence (less color and more black), while a larger tolerance equates to looser guidelines and more points are considered converged (more color, less black). Auto-Zero: If this is checked, when the "Display" button is clicked, the program will automatically calculate the zeros for you, so you don't have to click both "Find Zeros" and "Display" to update the image. Leaving this button unchecked is useful to save time if finding zeros has a long processing time (high resolution and high iteration) and you want to display an image based off the zeros already calculated, such as displaying a gradient version of the same zeros without taking time to recalculate them. ---------------------------------------------------------------------------------------- Gradient Display: ---------------------------------------------------------------------------------------- These settings tell the program how to determine convergence for a gradient image after the zeros have been calculated. Tolerance min: This is the closest a point must be to zero in order to be considered COMPLETELY converged, or on a grayscale, true white. Tolerance max: This is the farthest a point can be from zero and still be considered converged, although on a grayscale, this is only one step away from true black. # of Gradients: This is how many shades of gray the program with compute. For a smoother transition between black and white, increase this value. Increasing the number of gradient shades increases processing time substantially. Auto-Zero: If this is checked, when the "Display" button is clicked, the program will automatically calculate the zeros for you, so you don't have to click both "Find Zeros" and "Display" to update the image. Leaving this button unchecked is useful to save time if finding zeros has a long processing time (high resolution and iterations) and you want to display an image based off the zeros already calculated. Colorize: Clicking colorize will take the last colored fractal produced and overlay ontop of the last gradient fractal produced. This will only work if both fractals were produced with the same resolution, but any other settings can be changed between the color and gradient version. Clicking the button a second time will undo the colorizing and display the grayscale version. Additional note on the "Colorize" function: Since colorize ONLY requires the resolution be the same between the color fractal and gradient fractal being overlayed, raising the number of iterations to 25 or 30 when computing the color version will show which zero the points are converging toward for all values of convergence with the gradient fractal. Reveal: (This button has two functions) Function 1: If it is clicked while a grayscale image is being displayed it will apply a different color to every shade of gray. This makes it easier to see exactly where one shade ends and another begins, although it only colorizes up to 10 shades of gray. Function 2: If it is clicked while a colorized grayscale image is displayed, it will show any portions of the color fractal that were covered up with black from the gradient fractal. ---------------------------------------------------------------------------------------- Color Palette ---------------------------------------------------------------------------------------- Each row in this section represents a color. The program uses colors as needed starting at color (1) and working it's way up to color (10). If the number of colors needed exceeds 10, the program will use the default color (dark blue) for all the rest. Each column represents a different color spectrum: R = Red, G = Green, B = Blue. The values of the color spectrums can range anywhere from 0 to 1, zero being absent (black) and 1 being most intense (white). For example, the first color's default setting is R=1, G=0, B=0, which displays the color red. ---------------------------------------------------------------------------------------- Status ---------------------------------------------------------------------------------------- Zeros: This status window indicates the amount of time it took the program to compute the last set of zeros. This window updates with a new shade of color everytime the user has the program find zeros, whether automatically or manually. The new shade of color is random so the user can tell if the program is finished processing at a glance. Display: This status window indicates the amount of time it took the program to compute the last image to be displayed. This window updates with a new shade of color everytime the user has the program calculate a new image, whether color or grayscale. The new shade of color is random so the user can tell if the program is finished processing at a glance. /--------------------\ | Author: Ian Cooper | \--------------------/