MIT is way ahead of you: gamelab.mit.edu/games/a-slower-speed-of-light . The twin paradox can be trivially explained by Doppler shift and signal delay, which is what observers are really seeing. The "paradox" only occurs because the naive argument with Lorentz transformations is neglecting that they are only valid for observers which are in the same location. For distant observers we have to use the Poincare transformations. I doubt that this insight is a matter of visualization. It's a matter of proper physics training.

I'd certainly welcome such an attempt. I think the difficult part would not be so much the math of it, but to come up with a concept that presents what's going on on a level that's intuitively understandable while being accurate, that doesn't look like a bunch of graphs. It would have to communicate the ideas of spacetime as a mathematical space, and of a simultaneity hyperplane as a slice through it.

What do you think an animation could show that still pictures don't show?

Does my answer here help? physics.stackexchange.com/a/719329/24362 The simulations are not "complete", whatever that means, but mimic the effects you would "see" as the traveller (aberration should be accurate, colour ind intensity effects are qualitative), and the scene is full of clocks. Make sure you view the animations in 1280 res, and read the info box (it tells you how all the clocks "work"). It is no longer as clear to see in the UI as it was when I first posted the videos.

It's unclear to me what you want to illustrate. Your other question says, e.g., 'the clocks attached to the destination star ten light years away "jump" from displaying "zero" to "ten years"', but I think you know enough about reference frames to know that's wrong. The clocks notionally attached to the star, representing the inertial rest frame of the star, always show that inertial frame's coordinate time. The notional clocks of the post-acceleration rest frame of the ship are flying past the star at almost the speed of light (and always have been). Is that what you want to illustrate?

I gather the core of the question is: for a traveller during phases of acceleration: how to represent the perspective of the instantaneously co-moving frame? A candidate for that is the animated gif available on wikipedia, titled Lorentz transform of worldline. The geometrical counterpart of Lorentz transformation is a scissor-like motion of the coordinate axes with respect to each other. See also: Momentarily comoving reference frame

@FlatterMann Note there are some major problems with that game, though not really relevant to this question. I don't see how one could get a better understanding of the twin paradox from the game. In principle sure, but in practice there's not enough going on in the game world. There's no way to set up a twin-paradox-like experiment.

@Willo An animation would show how the time indicated by a distant clock rapidly changes as the space ship reverses its direction of motion at the destination star.

@benrg You might be right. I was thinking that the clock on earth and the clock on the star are synchronized but in the post accelerational rest frame of the ship they are desynchronized due to being in motion in that frame.

For the traveller: the time indicated by a distant clock can only be observed with a delay corresponding to the distance. Of course, in the thought demonstration the traveller is an expert at application of special relativity, and the traveller can calculate what time-of-the-distant-clock he should attribute such that on rejoining the observed clock indication and the attributed clock indication coincide. The point is: an animation that faithfully renders transmission delay is difficult to comprehend. That is why all existing animations present the inertial point of view.

@Cleonis "in the thought demonstration the traveller is an expert at application of special relativity". I didn't mean to imply that.

What the observers in the twin paradox see are simply the Doppler shifted and delayed clock ticks of the other twin. When the travelling twin takes off, both see the same Doppler red shift. As soon as the travelling twin turns around his Doppler signal turns blue right away. The Doppler of the remaining twin stays redshifted for a while because of the delay between him and the traveler. In total the travelling twin's clock signal as received on Earth has fewer clock ticks than the Earth twin's Doppler shifted clock signal. THAT is the observational reality of the twin paradox.

@benrg I agree that a relativistic world simulation does very little to "educate" about physics. It merely looks funny. I have no opinion on the quality of the MIT game. The criticism certainly looks appropriate. My point was simply that people have done these simulations before. There are also similar simulations of black holes dives etc. which are also not particularly enlightening. Neither is "Interstellar", no matter how hard they tried. I did look into embeddings of general relativity manifolds as a student... it takes at least 10 dimensions to map things flat. That's 7 too many for me.

My only concern is when you say "animate a clock at each important location". What does that mean? The clock on earth is at a location on a earth, but it's at many locations in space-twins coordinates.

@FlatterMann "@benrg I agree that a relativistic world simulation does very little to "educate" about physics." Which statement by benrg are you agreeing with?

@JEB Also, things can be simplified by imagining almost infinite accelerations that last almost no time. Then the clock on the star will, for the ship, jump from indicating zero years to (plus) ten years in an instant as the ship accelerates from rest (earth frame) to close to the speed light.

@MatthewChristopherBartsh Are you learning Newtonian mechanics from looking at student experiments on the ISS? Sure, it is fun to watch astronauts who can float things around, but how much does that really teach you about Galilean relativity? Does a spinning ice skater really prove angular momentum conservation? These things are, at best, illustrations. They are not sufficient to develop an intuition and useful skills in the application of physics.

I don't think the difficulty is in making the animation. The difficulty is to make the animation possible for students to understand while at the same time be accurate. There would be too many things happening on the screen at the same time for students to reliably grasp what is happening. And this is before we talk about the time as measured by each twin, v.s. the time in clocks by every location, etc. The twin that accelerated, you would have to explain why you are trying to isolate the accelerating part from the non-accelerating contribution to time dilation.

@MatthewChristopherBartsh no, the ship frame is not many frames. It's two: out/in-bound. The point is you said clock "position", but the clock on earth/at star, are moving the ship frame. It's actually instructive to consider the times in all 3 frames for clocks at fixed positions in each frame. IIRC, the launch occurs waaaaay in the past for the inbound frame.

@JEB I figured that as the ship turns around it goes through an infinite number of velocities ranging from plus almost the c to minus almost c.