Fourteen Patterns

#1

Given only two colors (or on/off), there are 14 possible patterns of lights on a single Blink (that are unique up to rotation).* The relevant OEIS sequence is #A000031. I was wondering if there are any existing games that use these 14 patterns (or some subset of them) in interesting ways. I have been studying them and thinking about what can be done with them, but I’m curious to see what’s already been done.

*I find it interesting that Jonathan didn’t mention this fact in his talk at G4G14 when everyone else was bending over backwards to point out the connections to that number, but never mind that.

2 Likes
#2

Welcome!

Dispel uses them except for the degenerate cases of all-on and all-off. Look for patterns[] in the code.

Note that Face 0 is always assumed to be lit and Face 5 is assumed to be unlit. That’s why the data structure only has four bits per entry.

// Twelve possible patterns (not including all on & all off)
byte patterns[] =
{
  0b0000,   // 1
  0b0001,   // 2
  0b0010,
  0b0100,
  0b0011,   // 3
  0b0101,
  0b1010,
  0b1001,
  0b0111,   // 4
  0b1011,
  0b1101,
  0b1111    // 5
};
2 Likes
#3

I should also note that, in practice, Dispel only uses the first eleven entries in that array. The selected difficulty chooses the starting pattern (0-5). Then you can have up to six rune tiles, which just select the patterns in order from that array. So highest difficulty with six runes will use entries [5] through [10].

#4

It looks like a very nice puzzle, thanks.

1 Like
#5

Hey quintopia,

I am new to blinks and have been captivated by these things. One of the first test programs I created was a symbol enumerator to cycle through the 14 unique shapes with each click. This lead to the idea of a deck of cards - I created a simple card dealer which groups the unique shapes into 7 numeric values and 7 “suits” to make a deck of cards. 7 of the 14 shapes group nicely into a number sequence 0 to 7 (the shapes where the faces that are lit up and all touch). The other 7 make some easy to remember shapes (assuming you hold a blink with a face down and not a vertex): HourGlass, Mushroom(or Anchor), SwingLeft, SwingRight, Butterfly, Fangs, and Toxic. It’s easy to alternate the suit and the number symbol to make each blink function as a card. My family and I now play Euchre with blinks using this setup and 4 of the suits (hourglass, mushroom, butterfly, and toxic). The “dealer” blink shuffles the selected cards and deals the value out to any blink attached to face 0. When you connect two or more cards together, they sync the animation so you get suits first, and then the numeric value symbol. Works great!

We have found that blinks make great cards and are easy to hold in your hand. With the ability to overwrite them with the “dealer blink” you need just enough blinks for your hand, the dealer, and one discard blink. We have simulated most of the classic card games this way. And you can now play cards in a dark bar or restaurant.

Cheers,
Dave

#6

:heart_eyes:
Feels like an opportunity to see some Blinks-card artwork… Illustrations? 8-bit art? Who knows… love the naming convention. Here’s a template to sketch some art :paintbrush:

Blinks_Card_Faces_illustration-template
Blinks_Card_Faces_illustration-template1776×926 34.2 KB

UPDATE: my initial swing right and swing left were missing a segment and as a result, simply rotations of each other. Also, the fangs was accidentally just a ‘5’.
Now they are unique.

#7

@sebswift great idea! it seems like you could also have a more normal deck with 14 values (7 of which are “face cards” with your named patterns) and 4 suits (colors–two hot and two cool colors).

@jbobrow these are not the patterns in question. the way you have them “mushroom” and “anchor” are the same. I think “anchor” is supposed to be the one you’ve labeled both “swing left” and “swing right”?

#8

I interpreted the Mushroom or Anchor as the same shape, but named depending on how you view it (i.e.180º rotated from each other)

I have a feeling my use of the “ON” color of white and “OFF” color of dark grey could also be cause for confusion. It’s based on the Blinks diagram standard.

#9

Rotations cannot turn any of the patterns into another. The fact that they are unique even under rotation is what limits them to only 14.

#10

Okay, after some further rereading, I think I’ve figured it out.

Jon is correct that anchor and mushroom are both names for the pattern he has labeled in that image.

The ones he labeled “swing left” and “swing right” are both what seb calls “fangs”

What seb calls “swing left” and “swing right” are what you get when you turn the bottom face on in Jon’s corresponding images.

What jon’s image calls “fangs,” seb would just call “5”.

As far as existential complements go:

Number n is the complement of number 6-n.

Hourglass is the complement of butterfly.

Swing left is the complement of swing right.

Fangs is the complement of mushroom/anchor

Toxic is its own complement.

1 Like
#11

I think the diagram updated now reflects the non-number patterns correctly. I added a note that is is now updated.

1 Like
#12

Hey, Yes, diagram is right on! Thanks Jon. Mushroom and Anchor are the same thing (correct). Thanks for the drawing - I should have provided to make it clear.

I also like the idea of using all 14 for values (or 13 if you skip the blank) and using color for suit - you could get a full deck that way. I didn’t think about that- now I have some more ideas to think on. Although it may be hard to remember the numeric values above 6 - would need to think on that.

#13

hmm, maybe fangs and hourglass first,
then swing left, toxic, swing right,
then butterfly and mushroom.

that puts them in order from least on faces to most on faces, and also, the first is the complement of the last, second is complement of second last, and so on

toxic being the only self-complement obviously goes in the middle of the sequence, so left and right go before and after, and you can just remember left-to-right to know that left comes first.

then all that remains is to remember that fangs comes before hourglass–one way is to say hourglass is better because it has more symmetries than fangs.

1 Like