puzzle hunt 24-1:
detecting drinking water pipe damage

Doekle has built a pipe inspection robot that is to crawl its way through a drinking water pipe, scanning the walls for any defects. Occasionally, it parks at a wireless charging station, where it can unload data too, to be sent for analysis.

As there is limited storage at hand, Doekle has decided to make the robot send images in a 10×10 grid. This black-and-white image file is compressed into a couple numbers on the grid. The numbers represent cracks and dents in the pipes – these are white lines of pixels orthogonally (up, down, left or right) connected of a given size. You can think of them as islands of a size that contain and are the size of the number in the grid. All isolated from one another. So, for instance, the right-most two can only be centered on itself, and move one pixel up to be two pixels long and not branch to another island.

The rest of the pixels are black weave in between these cracks. All these black pixels are orthogonally connected in the whole grid. Think of it as one stream surrounding the island.

“To get the image back from this data stream is very simple,” Doekle says, “given that all islands are isolated by the stream. The only other thing you have to know, is that black pixels form one big web over the grid, but never form a solid 2×2 square. They are always interrupted at that by these islands in at least one of the four pixels that would form it.”

Please show off to Doekle and retrace the image from the encryption given below.

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