Judge's Notes on Blots

You may either view the judge's data graphically by looking at the images below or you can see where the images came from by recompiling the program with the display line uncommented:
(new DisplayCircles(disk, nDisks, dataSet)).setVisible(true);
If you compile and run the modified program, you get all the images in resizable windows that rescale, to allow you to get more detail if you want. The images come up with the last dataset on top. If you close any window, you END the program. To see other images, minimize or move the image on top.

Datasets 9-12 have circles of enormously varying radii. Not all detail is visible in the image of the whole dataset, so there are additional images showing details blown up, so all the circles and their intersections are clearly visible, below and in the program modified to display.

Judge's Data

Datasets 1-3 are the examples (not redisplayed here).


Dataset 4 1 unbounded region	Dataset 5 1 unbounded region


Dataset 6 1 unbounded + 2 bounded regions = 3	Dataset 7 1 unbounded region + 3*2 bounded regions on the outsides of the big circles = 7

Dataset 8: 10 rows of 10 circles making 6 patterns of holes repeated 9 times with 1 unbounded
region makes 1+6*9 = 55. (The circles are listed in the dataset in pseudo-random order.)

This dataset contains the component in Example 2 at a magnification of 10000 and 100 and 1. The smaller two components are translated to be just inside the space between the next larger component's four circles. In the largest and middle scale pictures you can barely see the next smaller component. Each of the three components encloses two bounded regions for a total, with the unbounded region of 1 + 3*2 = 7.

Dataset 9: All


Dataset 9: Detail in space between four largest circles	Dataset 9: Detail Inside the next four circles

Datasets 10 and 11 have exactly the same circle of radius 1000000 intersecting four circles of radius 10000, which each intersect a circle of radius 20. They differ only in four circles of radius 3 to 10.


Dataset 10 and 11: All (look alike at this scale)	Dataset 10 and 11: Left blob (Still look alike)	Dataset 10 and 11: Lower blob (Still look alike)

The most blown up details for Dataset 10 just barely show the curvature of the circles of radius 10000, showing they do not intersect.
Beside the region between the four circles, there is also the region extending between the circles of radius 10000 from the blockage of the four small circles to the circle of radius 1000000, off the pictures to the right. With the outer region, that makes 1 + 2*2 = 5 regions.


Dataset 10 only: Left Blob Detail	Dataset 10 only: Lower Blob Detail

Here the two tiniest circles do not connect with anything else to block off any bounded regions, so there is just the 1 unbounded region.


Dataset 11 only: Left Blob Detail	Dataset 11 only: Lower Blob Detail

Here the detail shows the region between the middle and the two lower circles. There is the outer region, plus the two regions by the top of the middle circle, plus the nine regions shown in the detail below the middle circle, for a total of 12.


Dataset 12: All	Dataset 12: Detail Below the Middle