I want to make an adapter that will take 4 1080p HDMI inputs and output 1 4K HDMI outputs to a 4K TV. Is this possible to do by just rearranging wires, or will i need to add in a Raspberry Pi or similar to translate the data?
No, you can't--you will need some kind of intermediary, and there may be considerations about processor throughput and latency. (I'm not qualified to say if a Raspberry Pi is capable of this.)
The reason is that your HDMI source of any type is transmitting digital streams of video and audio information. What you are trying to do is take four separate streams of video, composite them in a specific configuration, and generate a new video stream.
That said, there may be a much easier way to accomplish your objective -- perhaps if you elaborate a bit on what you are really trying to do, you may get a more useful answer.
The original question is reasonable and I offer this answer: a multiplexer (MUX) is a device allowing one or more low-speed analog or digital input signals to be selected, combined and transmitted at a higher speed on a single shared medium or within a single shared device. The MUX example is NOT 4K output:
This is signal processing problem and unless you have had the SIGNIFCANT required background / experience with hardware and software, it is unlikely you will be able to build such a device within a reasonable amount of time and cost.
Your time and money would be better spent by hunting for a commercially produced MUX. If you purchase such a device, please reply to share your decision