by Derek Kisman
At first glance, this appears to be a word search. And, well, that's exactly what it is. Hooray, word searches are easy! This puzzle should be a cinch! But wait... although you can find a few of the words in the given grid, most of them are missing. Where could they be?
Well, if you examine the wordlist, the theme should quickly become obvious. This is actually a *fractal* word search. The given grid is actually just a single level of detail (level 2, in fact, as clued by the prominent LEVEL TWO near the top-left) of an infinitely-detailed fractal grid, generated by a simple iterative process.
Level 1 starts with an 11x15 grid:
LEVELONESSUPYPM EPATETATIMSAORQ SKFAICRDPCAWHWH CONKBAHEAUEHRUA IYMANDELBROTRDU NTRGIHIYLLARSES OLEIZNEAHIIZKVD TFHRGVWCVCLHHLO CHPSAELOAUUXTMR EBGWATRNREJAKPF TSQUARESSBPOCTF
Each successive level, twice the width and twice the height of the previous level, is formed by replacing each letter with a specific 2x2 block of letters:
A B C D E F G H I J K L M TF GO IR HI EL CG RP UE BW PK OZ TW NL JM DN HK JU PI UH AJ BN AO DF VQ QA OR N O P Q R S T U V W X Y Z SH ON RA WJ YD MU DT OE EV NC EY IY LM PE YD OY FC AN RP HA KV UN ZK HW ES GI
You can figure all of this out by noticing that the given grid has many repeated 2x2 blocks - in fact, there are 26 different blocks. Working out which block corresponds to which letter requires solving level 1 in a cryptogram-like process. You just need to make use of the fact that many of the words (a majority, in fact) show up in the level-1 grid. LEVEL ONE is also placed in the top left corner as an aid, although it's not strictly necessary to notice this. There is plenty of redundancy.
However, even after doing all this, some words will still be missing. That's right: you'll need to delve deeper into the fractal to find them! There are words hidden at levels 3 and later. But the grids get very large very quickly. Searching the entire grid by eye will probably fail for levels 4 and up; and even a naive computer search will fail around levels 7-9. Cleverer methods are needed - analysis of patterns, or more targeted computer searches - to find all of the words. The last word is hidden on level 86, which is a 425,541,888,504,349,469,496,573,952 x 580,284,393,415,022,003,858,964,480 grid!
Here are the levels each word is on, with brief expansions to show you roughly where they are.
Level 1 (18 words):
LEVELONE....... ............... ............... ............... ..MANDELBROT... ............... ............... ............... ............... ............... TSQUARE........ ....L.......... ...TE.......... S..AI....C....H C..KB....U....A I..AN....R....U N..GI....LA...S O..IZ....II...D T........CL...O C........UU...R E........EJ...F T.............F ........S....P. .......T..S.O.. ......R..C.W..H .....A..A.E..U. ....N..L.R..R.. ...G..I.L..R... ..E..N.A..I.... ....G.W..C..... ........A...... .......N....... ......E........ ............... .....T...M..... ......R...A.... ..N....E...H... I..A....B...R.. .T..I..Y.L...E. ..E..N..H.I...D ...R..W..C.H... ....A..O..U.... .....T..R..A... ......E..B..C..
Level 2 (6 words):
I B.
H -> .O
T U.
P .N
D.
.A
R.
.Y
F ..
H -> .H
B .E
.N
.O
.N
EVELO -> .LEVELTWO
.........
IM ..N.
DP -> .O..
HE ..R.
.U..
..E.
.N..
CVC -> .REVIR
......
YM .Y..
RG -> ..O.
IZ .D..
..A.
.W..
..G.
Level 3 (3 words):
ZK .M.. ..
HL -> ..V. -> .R
.E.. E.
..Q. .N
E.
.I
W.
..
H U. ..
N -> B. -> .V
V S. .O
P. .N
E. .U
.. .P
.A
.Y
.L
..
V .. ..
PA -> .N -> .E
..TF ..C.
.YJ. .A..
..P.
.S..
Level 4 (1 word):
P .. .. E.
KF -> .Y -> E. -> .I
.ZC. .M.. N.
.... ..H. .R
U.
.N
Level 6 (1 word):
RQ -> .DW. -> .... -> .... -> EVRPBW -> .LEVYDRAGON.
.... .UZ. .VGI ...... ............
Level 15 (1 word):
PY .... .... .... .... ..E.
A -> .YE. -> ... -> .SO. -> .PY. -> .YE. -> .S..
.F .P RA ..TF ..C.
.. .. .. .NJ. .A..
..P.
.E..
Level 17 (1 word):
GW -> .. -> KL -> .. -> JW -> .. -> GL -> .. -> KW -> .. -> JL -> .. -> ..
JZ .. QQ .. FZ .. JQ .. QZ .. FQ HF
..C. .. .. ..
-> .NU. -> H. -> B. -> .N
.HO. .EO. ..O.
PE.. BN.. .I..
.AE. ..S.
OY.. .N..
..E.
.M..
..I.
.D..
Level 86 (1 word):
H .. .. O. ..
PS -> .N -> ... -> .U -> KV -> Y.
.AM. .GN. .PS. .Z..
.... .... .... ..U.
.A..
..R.
Before you find all the words, you'll probably note that another typical word search trick applies: the "leftover" letters on the level-1 grid form a message. Mind you, the definition of "leftover" isn't quite as straightforward as normal: if any portion of a letter's expansion ever contains part of a word, you need to strike that letter out. (Technical note: this definition specifies a unique location on the level-1 grid for each word. However, due to the nature of the iteration, some of the deeper words actually appear periodically, rather than on one specific level. But no matter which level you look at, they still touch the same level-1 letters.)
_________SU___M E_____A________ _____C______HW_ _O__________R__ _____________D_ ____________S__ _L____E______V_ _______________ _____EL____X_M_ ____A_R_____K__ _______SS_PO_T_
The hidden message is: "SUM EACH WORD'S LEVEL. X MARKS SPOT." The final extraction should be clear. Find each word and note the level on which it appears (naturally, for periodic words, you use the minimum level). Add them all up to get 167. There is only one X on the level-1 grid - used for the message! - and it doesn't appear anywhere else in the fractal. Expand the grid to level 167, look at the center of that X, and you'll see the answer, in an X shape:
H..Y
X -> EY -> ... -> DY -> .UE.
HW CS .RM.
H..P
The final answer is HUMPHREY.