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Please pardon my lack of proper etiquette here on this platform.

I'm trying to articulate an equation, perhaps a vector, that expresses an object that's scaling down towards zero.

For example. In the movie "Honey I Shrunk the Kids". The kids were scaled down in size by some factor. If they kept scaling down further and further tending towards zero it could be thought of as distance. In this case zero is an infinity as it can never be reached as they can always scale down further more in size. Such a journey would move them towards the Planck length and eventually past that as they journey further towards zero.

Thus how do you articulate such a thing as an equation that is a function of a scale factor and time?

Also this is not for homework.

Thank you all.

Tivity
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  • I don't agree to downvote this question which is indeed a little vague but displays a real synthesis attempt. – Jean Marie Sep 05 '20 at 15:29
  • It's hard to answer to your question. 2 little thoughts: 1) if you want to establish a relationship between distance $x$ and time $t$, you can imagine that the shrinking speed $v$ is a constant. Therefore, as $v=\dfrac{x}{t}$, you can restrict your attention to functions verifying $f(x,t)=f(ax,at)$ for any $a$, functions which can be vector-valued if necessary... 2) you should maybe look into the direction of objects that shrink whil "remaining the same" i.e. fractals, each fractal having its specific dimension. – Jean Marie Sep 05 '20 at 15:36

1 Answers1

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This is an Affine transform called scaling, where for an image centered on the origin any point ${\bf x} = (x_1, x_2)$ in the image is mapped to ${\bf x}^\prime = \alpha {\bf x}$ for scalar $\alpha < 1$.

David G. Stork
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