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Here is a sample I made for the first GIF because the original is way too large to send. https://pasteall.org/blend/0cf6eb4715e34404b5299906408c2964

This is just a simple version of what I'm working on. As you can see in the GIF below. I am making a seamless loop and for some reason the scaling speed is fast in the beginning and slows down to the end of the timeline. I have the smallest cube parented to the next biggest and so on, and the biggest cube is parented to an empty. I'm scaling the empty from 1 to 3x the size and the key frames are set to linear, but there is still an easing look to the animation. Do you have any idea why that is? I thought the scaling speed would be consistent if set to linear.

enter image description here

enter image description here

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What you see here is totally correct. Scaling in the beginning "looks" for our eyes "quicker" because from 1 to 2 you get double size. But from 2 to 3 it scales only 1/3 of original size. And so on. So it as a matter of fact scales "slower" if it has bigger values. So if you want to keep the "original" scaling speed, you have to double the scale each timeframe. So if your time frame is 1, 2, 3, 4, 5 your scaling values must be 1, 2, 4, 8, 16

to get what you want you can use a driver in your scale with this scripted expression:

(frame/10)**2/5

where you can change the 5 -> this is your scaling speed

Here a visual comparison of linear speed, to linear scaling and quadratic scaling.

enter image description here

The quadratic scaling should "look" for our eyes as a constant scaling - although mathematically it isn't.

enter image description here

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    $\begingroup$ Good catch ! These motion graphics effects are all about trumping our perception, so it's only fair that the solution is to cheat a little bit to achieve the result ! :) $\endgroup$
    – Gorgious
    Mar 10, 2022 at 8:20
  • $\begingroup$ I am even not sure if it should be **3 ….because it is a volume. Area should be **2 🙈 $\endgroup$
    – Chris
    Mar 10, 2022 at 8:33
  • $\begingroup$ The reason I had to scale it up by 3x is due to the cube being divided into a 3x3 cube. If I did 2x, then the next 3x3 cube would not match the same position as the previous cube. I am confused by a few things you mentioned. I don't understand this line "So if your time frame is 1, 2, 3, 4, 5 your scaling values must be 1, 2, 4, 8, 16". Are you saying time frame as in the frame number? If so, then the cube will scale up way too fast before half a second is played. If you can, pls dumb it down because I'm a visual learner and it's hard for me to understand what I'm reading, sorry. $\endgroup$ Mar 13, 2022 at 14:41

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