Time for Something New

Question

^{An entry in Fortnightly Topic Challenge #23: Seasonal...}

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Today, when you go to your mailbox, you find a thin card-sized envelope from your (in?)famous uncle—a games and puzzles creator of dubious skill and legendary absentmindedness, who you now reflect didn't send his usual holiday card.

You open the envelope to find a simple card with colorful confetti, ribbons and balloons on a black background. But when you open it, instead of the expected felicitations, best wishes, and apologies for being late, you find this:

       

Constellations? Connect-the-Dots? Nothing leaps to mind to explain this unusual card. On a whim you turn the card over to see which greeting card company created it. That's when you see this:

0) Bottom. Left.
1) By twos. (Then by fives.)
2) Case matters: upper case is upper; lower case is lower.
3) Connect the dots.
  A + D0AAa Aaa0a FxFVF vFXaA
  B + FLaAa AbhDf DHBOa AaAaa BwAaD LBBAa
  C + AhAaC CABBG BBAa
  D + AhAaC CABaG aABbB aAAAC bnAEB GBBAa AcbjA EBGBB AaAcb iAaCC ABCGa AaAbh DfDH
  E + BBHDH dprbb R0
  F + AFBBC BDBDb CbBbA fafbb cbdbd BcBbB aF
  G + DH0x
  H + L0
  I + BDN0b fllbf
  J + bDBDB dbd
  K + dJBFB BBbBf dj
4) Have fun!

What is the meaning of this card?

$ $  

Hints

helpfulness level 0:

Already given: an earlier edit added a single word, which helps somewhat.

helpfulness level 1:

H + NT = $\scriptsize\vec{\bf{HI}}$

helpfulness level 2:

Understand helpfulness level 1 Hint and you should easily solve this.

Answer 1

Prologue

I will start by explaining what each rule means

0) Bottom. Left.

This rule declares the origin to be the bottom left, giving an immediate unambiguous definition for addition (up and right are positive; down and left are negative)

1) By twos. (Then by fives.)

"By twos" refers to the text: we take two characters at a time (more on this later). "By fives" refers to pixels: we mentally grid the image into five by five sectors. This pleases Faith Lehane.

2) Case matters: upper case is upper; lower case is lower.

This is very clear: upper case means we move in the positive direction (away from whichever axis), while lower case means we move in the negative direction (towards whichever axis)

3) Connect the dots.

Explanation below

4) Have fun!

Oh come on, this is a gimme. You didn't need to read this spoiler. It's quite literally telling you to enjoy the puzzle. I didn't need to spell this out for you.

$\color{red}{\textbf{From here on out, no more spoilers except for the final image.}\\ \textbf{Proceed at your own risk.}}$

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Okay, Will, but how do you connect the dots?

Let's take a look at hint:

H + NT = $\scriptsize\vec{\bf{HI}}$

This cleverly uses the letters H, I, N, and T, but that's a red herring. A red herring in a hint, kinda mean I know; but hey, I didn't write it and anyway I think it's amusing. Nice one, Rubio.

So here's the scoop: H refers to the dot. We use A1Z26 to turn N and T into $14$ and $20$, and move that many grid units in positive directions (the N and T are both uppercase!). This means that – starting from point H – we move $14 \times 5 = 70$ pixels to the right and $20 \times 5 = 100$ pixels upward. Hey! That gets us to dot I. We've drawn the vector $\scriptsize\vec{\bf{HI}}$.

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Okay, Will, I got that, but NT is only two characters, and they're grouped in fives

Another red herring. Wow.

Just take them in twos and ignore the spaces.

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I will not show all the arithmetic I did to arrive at the answer. It's long and boring. I may be persuaded to post a short example, like A or C (though probably an ever shorter one) if you ask nicely.

Here's the final image we get from "executing" each line on the card:

We're done. Yay.