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Star Trek TOS has (at least) two computers with round screens, the M5 and the Beta 5 described below. This is an out-of-universe question on the design of the props.

Both remind me of the early PDP computers shown in this question but I don't know if it is just a coincidence (round CRTs were more common then perhaps?) or if inspiration was really drawn from real computers of the time. Is there any information on this, or perhaps on the people who designed the computers for the sets of these episodes?

I'm also interested if there is any information on the artistic design of the moving/drifting wavy lines, projected onto the round screen of M5 and in the upper rectangular screen of the Beta 5, and the rectangular displays with fixed, thin rectilinear color lines. I could ask that separately if someone expresses an interest in answering separately.


M5 (The Ultimate Computer)

From this answer:

In the TOS episode The Ultimate Computer the famous scientist Dr. Richard Daystrom (namesake of the Daystron Institude) has a mental breakdown after the M5, closely modeled after Daystrom's own mind, had committed what Daystrom felt to be murder by intentionally destroying a Starfleet ship as part of an exercise gone wrong. At the end, Daystrom needed to be taken to "a total rehabilitation facility".

Screen shot from Star Trek: Daystrom Speaks to The Unit:

enter image description here

Beta 5 (Assignment Earth)

The Beta 5 Computer

...was a sophisticated computer built by unknown aliens from a hidden planet located more than 1,000 light years from Earth. It was installed in 1968 at 811 East 68th Street, Apartment 12-B in New York City, which was occupied by pseudo-secret agent Gary Seven.

Screen shot from Star Trek - Missile Alert

enter image description here

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    As similar circular screen appeared a few years later in the Doctor Who story "The Green Death": tardis.wikia.com/wiki/BOSS – Buzz Jan 2 at 6:14
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    Both computers are in fact the same prop redressed between the two episodes. I couldn't find any information as to where the idea came from on the usual Trek sites though. – Sava Jan 2 at 7:13
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    Added an answer with the PDP-6 from 1964 and then deleted it because I noticed you mention it in your question. That's what I get for trying to post an answer while eating breakfast and talking on a conference call at the same time... – LAK Jan 2 at 14:40
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    @LAK that seems like a pretty lay-back SE site, I don't think anyone would have objected. If you can add a bit about what the screen was for, that would be fine. If you'd like me to delete one of the photos in the question so you can use something similar, let me know also. (except the first photo, I'm fond of it; oh wait that's the PDP-6). You can send me a link to your deleted answer if you'd like me to have a look. In any event, thanks! – uhoh Jan 2 at 14:44
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    More a case of Life Imitating Star Trek, but the swirling display on a round screen certainly seems to survive in the "display" of IBM's Watson computer system - thumbs.gfycat.com/… – VBartilucci Jan 2 at 19:42
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You have asked two questions.

Who designed the props?
I have no idea.
Sorry

What inspired the circular computer screens?
This I can answer with some small degree of first hand knowledge. For this, you need to know a little about computer and electronics history.

A CRT is a Cathode Ray Tube. It works by sending a stream of electrons out, interrupted for ‘off’ pixels on the display. The radiation is directed by pairs of electromagnets, one pair to deflect the beam horizontally, and one pair to deflect the beam vertically. You can read more over at howstuffworks.com.

Very old equipment, such as an oscilloscope (link to Google image search) had an even coat of phosphorus on the display, and you could actually see the beam tracing back and forth (which was the point). Adjust the frequency low enough and watch for hours of fun. (Don’t be distracted by the square ‘lines’ — they were painted on the glass.)

The design was rather primitive, and a round screen was very much easier both to manufacture and to program for the bounds of the beam. Google finds pics of vintage TVs easily. The edges are rounded, not because of the signal encoding (the TV signal has always been for a rectangular image, IIRC), but because the image at the corners was either missing (cropped due to the bounds on the beam) or not very well defined (and hence fuzzy, and fuzzy is bad marketing).

More modern CRTs, like the stuff you grew up with in the 70s and 80s actually swept the beam much further than the (square) display, and had hardware to control turning the beam off past the edges, and a significantly more complex hardware for controlling the beam to strike the RGB phosphors in color TVs. (Get yourself an old EGA/VGA hardware manual if you want some interesting technical reading — you can control the bounds directly with software! :-)

Now, the idea of round displays was not new even with Star Trek. You can see round display screens in older sci-fi like Flash Gordon. Here’s a pic I found of an old FG comic featuring a round view screen. Looks a lot like an oscilloscope, doesn’t it? Image Round displays even featured in TV episodes along with the bleach-bottle ray guns.

During the late 40s and through the 50s, when people thought of hi-tech stuff, they thought of these cool devices that showed a picture. They thought of early televisions, which in the 60s still were new, high-tech stuff operated by nerdy science-y people.

Even today round is sleek and high-tech. I bet you can easily find many sci-fi movies featuring pretty, round/curved, holographic/see-through/awesome futuristic displays, with no square corners, all on your own.

Moving, drifty, waving lines
Simply, money. Oh, and corporate aesthetics. Psychadelic, cool stuff doesn't look like the text-graphics computer displays in the Andromeda Strain. Andromeda Strain.

Star Trek (TOS) was shot on an exceedingly tight budget given what they were doing. Masking part of an image to place another above it was a time-consuming technique. Doing things like lining up a spaceship against a planet was an expensive task. Why spend time and money to display something that we would consider ‘real’ that had no effect on the plot? It was much easier to simply put up a pretty color wash that got perfectly cropped by the masking.

Even if Spock had to look into the display and ‘read’ something, it wasn't too far-fetched. A lot of old optical equipment could only properly display things to people directly in front of it. Those in the audience’s position would not see anything more than colored light. I suppose that on Star Trek the displays were just more advanced so you got a lot of colors. That or it was a screensaver, LOL.

tl;dr
So, to finish, the main points are:

  • It wasn't really new, just pretty and more futuristic versions of stuff we already had
  • It was cheap and easy to produce that way

Enjoy!

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    oscilloscopes, +1. Spock is looking into a Optical comparator the whole time. – Mazura Jan 3 at 2:41
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    Maybe I'm too nerdy, but I think the Andromeda Strain image looks cool too. – JAB Jan 3 at 3:48
  • @Mazura Yes, the optical comparator on the bridge was cool science-y stuff. – Dúthomhas Jan 3 at 15:40
  • @JAB The graphics displays from the Andromeda Strain were very advanced high tech stuff for the time, and figured into the plot as demonstrating how advanced the underground installation was. It was extra cool. :-) – Dúthomhas Jan 3 at 15:42

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