I made this challenge as a play on the Arecibo Message that we sent out into space in 1974 to announce our presence to the universe. Having the wikipedia page of the Arecibo message open while solving mine was pretty much essential.
Like the original mine had a semiprime number of characters which was 1357=23*59. There are two ways to lay this rectangle out, but if you try going for landscape rather than portrait then you will get meaningless static (probably, I haven't tried). Also noting that the original was 23*73 suggested that 23 across was a good bet.
Laying it all out in the rectangle was easier if you automated it, but wasn't hideous to do manually. Here it is:
And here's the original:
Our goal is to work out who sent the message and we are going to start at the top and compare the parts to see what is different. The first thing establishes the number system as base 10 which suggests the sender has 10 digits. Each number has a block at the bottom and then encodes the number in binary above it.
The next part down should have been the common elements making up the body. However there are two blocks on mine. By using the numbering system from above we get the numbers 6, 14, 26, 29, 30 and 79 for the left block and then the same numbers in a different order, 29, 30, 26, 14, 6 and 79 on the right. Taking the original as inspiration we can interpret these as atomic numbers giving us Carbon, Silicon, Iron, Copper, Zinc and Gold for the left where they are simply going up in ascending number. On the right the order becomes Copper, Zinc, Iron, Silicon, Carbon and Gold.
What could I be trying to say with this second order? I put them from most common in the body to least common. This suggests we are looking at a metallic based body, possibly with some electronic components because of the copper and the silicon.
Normally the next part of the message would be the common compounds found in the body to make DNA, so I used this bit to just show off some general compounds found in the sender. Using the same style as the original (see the wikipedia page for more detail) the left compound is made of 3 Copper atoms to every 2 Zinc which is Brass. The right has 1 Carbon to 3 Iron which is Steel. This gives us more clues for the make up of the body.
Normally we would have the structure of DNA. Its absence hints that DNA might be missing from our particular sender.
Next we have the height and shape of the sender. This is identical to the original so it is a humanoid, however with the population I have encoded the number 1, which means that there is only one sender.
Then we have the solar system. Two Stars on the left and a smaller planet which is raised indicating that is where the sender lives which has three moons. Then further out we have two larger planets, presumably gas giants, which have another seven moons between them. Clearly the interesting thing here is the binary stars, which, while common in the universe, are unusual enough in fiction to be a major clue.
At the bottom we have a picture of the parabolic dish which would send the message and it is identical to the original.
Putting it all together we are looking for a humanoid robot (where both brass and gold have been mentioned) that is on a planet with two suns. C3PO, I do believe you are the droid we are looking for. I had to take some artistic licence with the chemical make up of his body because for some reason the half dozen Star Wars wikis that I tried didn't deem that important information. The solar system was Tatoo system which contains within it Tatooine.