Astroid_Mset Part 2 - Parameters and Modifications

The main parameters that need to be adjusted are the width (real part of p1) and radius (imaginary part of p1). In order to get the formula to work properly, the parameters need to be within a range that avoids a few pitfalls. The width adjusts the thickness of the curves. If the width is too thick the curve will be totally filled in and not an astroid at all. The radius adjusts the overall size of the curves. If the radius is too small the curve will also be filled in. If the radius is too big what usually happens is an astroid from somewhere off the screen obscures the area you are trying to see. If you get a solid color screen try reducing the radius to see if that fixes the problem. The other parameters in p2 allow you to match the color table with the formula. You will never need to adjust these unless you want to change the number of color ranges in the color table.

The image mosaic at the top shows what happens when you adjust the radius between 0.6 at the top left and 0.1 at the bottom right in increments of 0.1. Our image from yesterday is the one in the upper right. The upper left tile shows a red astroid that has come into the image from the left and is overlapping the minibrot in the center. Notice that the red curve is much thicker that our yellow astroid. A lot of the time a very thick offscreen astroid covers the entire image. As you can see from the images across the top the red astroid moves out of the way as you reduce the radius.

The center image on the bottom is a noteworthy case. When you adjust the radius and width to just the right values, the tips of the astroid elongate and touch the center of the minibrot. This is useful for zooming into a minibrot you can't see. The bottom right case shows when the radius is just too small for the width you are using. Either increase the radius or reduce the width.

Now a quick explanation of why I changed the Astroid_Mset formula. There was a change to FractInt after version 19.6 that affected the clamping for several of the coloring methods including outside=summ that is used by this formula. The result of the clamping change causes the background color to be assigned to color index 1 instead of the intended color index 0. Color index 1 is already used for one of the astroid color ranges. I changed the formula so that it moves the background color to the unused index 254 to avoid this problem.

It is fair to mention that the original formula would work if you run it with the old version number as reset in the parameter file. But, if you look through the mail list archives, you will find several cases where people posted the old formula with the new version. So I thought it was worth updating the formula to use the conventions of the latest FractInt version.

In Part 3 we will see what happens when the Astroid_Mset is applied to one of Jim Muth's Fractal Of the Day images.