One can buy cheap 4K TV's these days for change of $200. The one above is a Hisense 43" with built in Roku that I got from Walmart in the January sale for $179. Below it is one of my work 37" wide screen monitors.
So basically the Geochron 4K clock is a bit of software running on an embedded device of some sort. I've not seen one up close but it looks like it might be some sort of AndroidTV Set Top Box? It's able to display the greyline, track satellites and do other things in that vein.
Looking around the Internet I found this piece of software by Simon Brown (of Ham Radio Deluxe fame). It displays a greyline graphic in real time onto your PC screen. It can also show you a handful of other details such as the Solar Indices and multiple clocks. The picture can also be changed for one of your choice.
In the junk pile I have an Intel Compute Stick. It's a 1.4GHz quad core PC that one shoves into the HDMI port of your monitor. It runs Windows 10 and has 2GB of RAM and 32GB of storage. It's also 4K capable.
Within minutes I had it up and running and displaying the greyline clock. I have configured the Compute Stick to automatically run the software upon power-up and so if I want to watch the clock I simply turn on the TV.
The total cost for this project (assuming everything was bought new) is as follows:
43" 4K TV = $180
Intel Compute Stick = $120
Software = FREE!!!
TOTAL = $300