At the tangency of the first and second disks.
13.
As the larger image of the Mandelbrot set shows, one passes through a sequence of tangent disks that get rapidly smaller as one moves to the left. At the end of this sequence is the point called the Myrberg-Feigenbaum point. We will show a few Julia sets as c moves toward the Myrberg-Feigenbaum point. For these next images, the image of the Mandelbaum set is also clickable. This leads to an enlarged image of the region of the Mandelbrot set near the appropriate c value. You will notice that the smaller disks are similar to each other in their attached "buds" and filaments, but they are not identical. As the Myrberg-Feigenbaum point is approached, the filaments get larger and more "tangled looking." It turns out that the image of the Mandelbrot set near the Myrberg-Feigenbaum point is very hard to compute. In fact, the structure there is not very well understood. This is discussed further in the section: The significance of the Mandelbrot set.
We give more information to go with the images of the Mandelbrot set pieces. Each detailed image has the point c as its center. We give a radius which is the distance from the center of the image to each of the sides.
We also give information related to the coloring. We still use up to 240 colors to color the approximating bands, but we may either use one color to color several adjacent bands, or we may skip some colors to make the bands more distinct. We may also start our coloring with a band other than band number one. The information that give this is a "skip" value that tells the number of the first band colored, and a number that tells either the number of bands that are given one color ("bands/color" - used when there are more than 240 bands in the image), or the number of colors that are skipped between adjacent bands ("colors/band" - used when there are fewer than 240 bands in the image).
Except for the image at the Myrberg-Feigenbaum point, the full color images of the Mandelbrot set on this page are from 33,000 bytes to 64,000 bytes.
c=-1.25+0i, radius=0.153, skip=8, bands/color=1.
At the tangency of the first and second disks.
13.
c=-1.309375+0i, radius=0.094, skip=11, bands/color=1.
Near the center of the second disk.
14.
c=-1.3681640625+0i, radius=0.0347, skip=18, bands/color=1.
Near the tangency of the second and third disks.
15.
c=-1.38115234375+0i, radius=0.02056, skip=23, bands/color=1.
Near the center of the third disk.
16.
c=-1.394140625+0i, radius=0.0.00754, skip=37, bands/color=1.
Near the tangency of the third and fourth disks.
17.
c=-1.4011551892+0i, radius=0.000001, skip=1468,
bands/color=120.
At the Myrberg-Feigenbaum point. The full
color Mandelbrot image is of a very small area, and over 30,000
bands are used in the coloring. The compexity of the Mandelbrot set
near this point can be seen. The image is large (318,000 bytes).
18.
Forward to What is the
Mandelbrot set - Page V (6 embedded images).
Back to What is the
Mandelbrot set - Page III (10 embedded images).
Back to The Mandelbrot Set and Julia Sets.