16

This puzzle belongs to the puzzle series: hyper-modern art

After solving the message in the butterfly image, the two friends move on to the next room.

"This was certainly an overwhelmingly large picture in the last room. Can we have something smaller please?"

"Sure. Just look over there on the table..."

"Is this a microscope?"

"Indeed it is. Just look through it. My guide states that the image under investigation consists of exactly 93635 square dots created by laser-printing on only a square-millimetre of paper."

"Hmm, certainly an interesting image, although not as beautiful as the last... What is it called?"

"It's called Homage to LA."

"Well, then there certainly isn't something secret about this one. You can clearly read this!"

"Yes, but do you also know what L A stands for? And remember: It wouldn't be a piece of hyper-modern art if there wouldn't be an unambiguous solution to this held within the image itself!"

PuzzleImage

The goal of the puzzle is to find some message - other than the obvious text - in the image, which will be a clear hint to the solution what L A stands for. A complete answer contains this message, how it can be found, and what L A stands for. The puzzle is fully contained in the image. The story is just flavour...

CalvT
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BmyGuest
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  • Does this require me downloading the images and messing with the RGB to get what appears like some text above homage? – qwertylpc Jul 16 '15 at 18:08
  • @qwertylpc I believe with most stenography puzzles you will need to download the image to be able to properly investigate it. Whether the answer lies in changing the RGB values, I'm not sure. – Mark N Jul 16 '15 at 18:16
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    @qwertylpc the steganography tag is pretty detailed in it's description. It's pretty safe to say that you won't find the answer to this problem just looking at the image. – LeppyR64 Jul 16 '15 at 18:24
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    (Also looking back on the series and the poster this puzzle could be quite complex) – LeppyR64 Jul 16 '15 at 18:27
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    If I let my eyes go out of focus I see a UFO and a dinosaur :P – dennisdeems Jul 16 '15 at 18:50
  • Yes, thorough image analysis is required. However, the puzzle is solvable by an image (at pixel level), as our two friends just look at the image. They don't have the binary representation... (But having one, might be easier to analyse ;c)) – BmyGuest Jul 16 '15 at 20:14
  • Can you tell us what font you used in this image? – Stephen Donecker Jul 23 '15 at 00:18
  • I believe it was the windows default TimesNewRoman or Arial, but it is not important to the puzzle. – BmyGuest Jul 23 '15 at 07:21
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    I wonder if it is needed to add a hint (or rather do a slight edit to the image such that it contains a hint.) I will not do this now, but if enough people upvote this comment, I will. – BmyGuest Jul 23 '15 at 07:23
  • Since the font is not important to the puzzle, can we conclude that the number of similar color pixels touching the letters, the character spacing, or vertical alignment is also not important to the puzzle? – Stephen Donecker Jul 23 '15 at 16:16
  • @StephenDonecker I don't think one can logically conclude this, but neither of the mentioned is relevant for the puzzle. :c) The whole steganography part is not overly complex. Think simple first. – BmyGuest Jul 23 '15 at 18:07
  • Could the typical person decode this puzzle in their head (knowing the solution method), or does it require pencil and paper or a calculator? – 2012rcampion Jul 24 '15 at 03:05
  • @2012rcampion Tricky question, as "in their head" is very subjective. It does only requires primary-school maths though. (Well, I'm not 100% convinced that all mathematics is thought in primary-schools all over the world, but it was in mine :c)) – BmyGuest Jul 24 '15 at 06:18
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    There are 19 unique colours in the image. I split the image into each of it's colours. If anyone is interested in looking at the pictures I have posted them here: Google Drive for Images There are the 19 PGM files which are colour and labelled with the RGB values. There is also a photoshop file with all of the layers and transparency for twiddling them on and off. – LeppyR64 Jul 22 '15 at 10:12

2 Answers2

19

Following Leppy's lead, here's an animated .gif with all the layers in order of hue.

enter image description here

The 19 colors themselves are fully-saturated and evenly spaced around the edge of the color wheel, suggesting a kind of sequence.

enter image description here

Numbering the colors from 0 (red) to 18 (magenta) we have the following numbers of pixels of each color:

color # of pixels
0 4963
1 5338
2 4317
3 4934
4 5617
5 5067
6 4955
7 5396
8 4554
9 4893
10 4698
11 4816
12 4259
13 5004
14 5015
15 5033
16 4906
17 4770
18 5100

Taking each one of these numbers mod 26:

23 8 1 20 1 23 15 14 4 5 18 6 21 12 23 15 18 12 4

Converting these numbers into letters (1 to A and 26 to Z) gets us:

WHATAWONDERFULWORLD

...the name of a song by:

Louie Armstrong

Mathematica code to solve the puzzle:

FromCharacterCode[
 Mod[Last /@ 
    SortBy[Tally[
      Join @@ Import["https://i.stack.imgur.com/feRTC.gif", 
        "RGBColorArray"]], First@ColorConvert[First@#, "HSB"] &], 
   26] + 64]

...and to generate similar puzzles:

message = "ITSAWONDERFULLIFE";
cover = "Homage\nto\nJS";
n = StringLength[message];
colors = Round[List @@@ ColorConvert[Hue /@ (5/6 Rescale@Range@n), "RGB"], 1/255];
counts = ToCharacterCode[message] - 64;
{w, h} = Catch[Do[
           If[Mod[w h - Total[counts], 26] == 0, Throw[{w, h}]],
           {w, 300, 500}, {h, w - 2, w + 2}
         ]];
data = Rasterize[
         Row[Style[#, RGBColor @@ RandomChoice@colors, Bold] & /@ Characters@cover],
         "Data", ImageSize -> {w, h}
       ] /. Append[Thread[255 colors -> Range[n]], {_, _, _} -> 0];
counts = Mod[counts - BinCounts[Join @@ data, {1, n + 1, 1}], 26];
zeros = Count[data, 0, {2}] - Total[counts];
counts += RandomSample@First@IntegerPartitions[zeros, {n}, Floor[zeros/n, 26]+{0, 26}, 1];
random = RandomSample[Join @@ MapThread[ConstantArray, {Range[n], counts}]];
i = 1;
data = data /. {0 :> random[[i++]]};
img = Image[data /. Thread[Range[n] -> colors]]

enter image description here

bobble
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2012rcampion
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  • Can you elaborate on the color circle part? I'm not certain what you're talking about. – LeppyR64 Jul 24 '15 at 01:52
  • @LeppyR64 Does that help? – 2012rcampion Jul 24 '15 at 02:03
  • It does. It's certainly interesting. What are the values that you use to calculate the position on the circle and what are the missing ones? – LeppyR64 Jul 24 '15 at 02:05
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    @Leppy I used Through[{Cos, Sin}[2Pi First@ColorConvert[#, "HSB"]]& to compute the positions in Mathematica. I don't know how it converts the RGB colors to HSB. The next colors, assuming they follow the pattern, would be #ff0085 and #ff003c. Although the spacing is uniform, it is not an even division of the circle: the 22nd color would not be pure red, but would be #ff0e00. – 2012rcampion Jul 24 '15 at 02:14
  • I really need to get myself a copy of that. It makes the stuff I do a lot easier. You have one command and I have 100 lines of code :) – LeppyR64 Jul 24 '15 at 02:37
  • I love this answer-post for its beauty, even if I will not tell if it is helpful for the solution. What would be helpful though (I think) would be some number-crunching, i.e. listing numbers derived in various ways. +1 for analysing the colour for order-sequence! (There is another way to determine colour-order in an 8bit indexed colour-image too. Do they match? :c) ) – BmyGuest Jul 24 '15 at 06:14
  • @Bmy Mathematica hands me the color pallette in hue order, is this the order that you intended? – 2012rcampion Jul 24 '15 at 13:54
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    @BmyGuest See here – 2012rcampion Jul 24 '15 at 14:15
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    I don't think the unused colors in the palette could be part of the puzzle. The rest of the puzzles in this series can be solved with a printed copy of the image, and it wouldn't make thematic sense for information to be hidden in that way. – f'' Jul 24 '15 at 14:18
  • To not chase people in circles: What I meant by my question from above was, that there is an order of colours based on the color-lookup-table of 8bit colour images - as shown in the link from above. This defines an order. However, it is the same order you also get by HUE alone. So to answer my own question from above: yes, the order matches. No other confusion about colours.... – BmyGuest Jul 24 '15 at 15:17
  • @f'' and 2012rcampion: There is a comment in the post which supports f'': Cite: <However, the puzzle is solvable by an image (at pixel level), as our two friends just look at the image. They don't have the binary representation... (But having one, might be easier to analyse ;c)) > – BmyGuest Jul 24 '15 at 15:19
  • @BmyGuest Let me be straightforward here. Are the 7 extra colors spurious or intentional? – 2012rcampion Jul 24 '15 at 15:27
  • A GIF 8 bit images always have 256 colours (the CLUT). These colours can be arbitrary RGB values. In the image at hand, they follow HUE range (as discovered). The 19 colours used in the pixels can be ordered by HUE (as you did) or by their actual CLUT-index. Both orderings are the same in this particular case. To answer your straightforward question: The image has 19 used colours and 256-19=237 "spurious" unused ones. They are also not used in the puzzle by the "look at image" argument. However, the discovered order plays a role. – BmyGuest Jul 24 '15 at 15:30
  • @Bmy Going back through your previous puzzles to look for clues... What a wonderful world of artwork you've created! – 2012rcampion Jul 24 '15 at 16:05
  • @Bmy I feel like I'm missing something... is that it? – 2012rcampion Jul 24 '15 at 16:34
  • Congratulations. Got it! :c) – BmyGuest Jul 24 '15 at 16:43
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    LOL, that's actually the first thing I did, didn't think to take it mod 26 though. Good work! – LeppyR64 Jul 24 '15 at 16:45
  • @Leppy It actually took me forever to get here. The structures Stephen found made me think the solution was row- or column-based... – 2012rcampion Jul 24 '15 at 16:48
  • @LeppyR64 Sometimes simple is hard ;c) The mod26 "trick" is needed to convert the idea of pixelnumbers=letters into something useful for images. It's still tricky to construct such an image though... (Needed some coding on my part.) And of course it does not work for arbitrarily sized images & messages. It can be applied to pretty large things though... – BmyGuest Jul 24 '15 at 16:49
  • @2012rcampion And for a good reason... I've exploited that idea in an earlier puzzle already though. ;c) – BmyGuest Jul 24 '15 at 16:51
  • @Bmy I found that one, and I tried to use it as a basis for the solution of this one... didn't work out, obviously =) – 2012rcampion Jul 24 '15 at 17:12
  • @BmyGuest Those poor guys and their microscope... – LeppyR64 Jul 24 '15 at 17:13
  • @LeppyR64 Na, they have HUD. They could count manually though... – BmyGuest Jul 24 '15 at 17:15
5

Solution

Liber Abaci

Details

At first we notice that the picture is made up of 19 unique 8-bit colors. Separating the image into 19 different images composed of one color each, we see that 10 of the images represent a letter in 'Homage to LA' with somewhat additional random noise while the 9 others appear to contain completely random noise. On further inspection we notice that the image containing the letter 'A' contains no pixels for the first 32 rows of the image which we assume is a mask for the other images. However, after a more detailed analysis we see that the image containing the letter 'L' appears to contain random noise in rows 17 to 32 with limited information in rows 1 to 16 which we conclude is a more specific image mask. Now cropping all letter images to the first 16 rows we begin to see our message. Summing the pixels in each cropped image results in an ordered series of numbers.

  • H = 192
  • o = 152
  • m = 117
  • a = 110
  • g = 96
  • e = 77
  • t = 54
  • o = 33
  • L = 18
  • A = 0

While searching for various number series I ran across Leonardo of Pisa, known as Fibonacci, who wrote a book in 1202 called 'Liber Abaci' known as 'The Book of Calculation'. In this book he describes many mathematical concepts but most importantly he introduces the Hindu–Arabic numeral system composed of digits 0-9 with positional value that we use today. This entire puzzle is possible because of him.

Jenia
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  • Not quite the solution, but on the right track. I like your rebus-like approach from the ASCII codes, but no, the hidden message is more obvious (and longer) than that. – BmyGuest Jul 21 '15 at 05:08
  • Ah, and BTW, your solution does not abbreviate with L A, does it? ;c) But still +1 from me to attempt a solution. – BmyGuest Jul 21 '15 at 06:36
  • In order to not alienate the above messages, you can view my original post in the edit log. – Stephen Donecker Jul 22 '15 at 04:25
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    Another interesting idea (and I've learnt something new), but not correct. The observation of the 'void' area is certainly interesting but don't get hooked on it too much. Some other idea in your answer gets you closer... BTW, I think it is better to start a new, second answer - if it is very different from your previous one - rather than completely editing it. Edits should only amend/correct things. There is no harm in having multiple answers from the same poster - they can be commented on and voted on and accepted independently. – BmyGuest Jul 22 '15 at 10:47
  • @2012rchampion The horizontal stripes found are an artefact of the algorithm building the image. The image is first build as "noise" and the letters where than added by "swapping" pixels. I should have done that in a more random fashion... What you're seeing is a "depletion" zone... – BmyGuest Jul 24 '15 at 17:14