Although it passes the time (which some of us have a lot of right now), there comes a point when Waldo’s innate ability to be hidden in plain sight crosses the patience threshold. How can a red-and-white-striped hat and sweater combo not be the first thing our eyes are drawn to? If only there was a quicker way to find Waldo, an optimal search method perhaps?
Well, data scientist Dr Randy Olson had this same thought and has done the hard work for you. Be prepared to inherit the Waldo wisdom.
For starters, Olson plotted the positions of Waldo in the 68 double-page spreads in which he appeared in the primary seven editions of the Where’s Waldo? books, created by English illustrator Martin Handford. By performing a kernel density estimation of the points (i.e. a visualization of the probability of Waldo appearing at a particular location, based on his previous hiding spots), Olson could draw a few conclusions.
Firstly, “Waldo almost never appears in the top left corner” – avid fans may recall a postcard from Waldo is usually placed in this position. Additionally, “Waldo is rarely at the edges” and in particular “never located on the very bottom of the right page.” Previous explanations for these patterns believe that the edges may be where people start their searches. Indeed the bottom-right hand corner may receive particular attention as that is where you might place your fingers to turn the page.
Already some top tips, but Olson took the project a step further by trying to devise the quickest path through the page, which visited all of Waldo’s previous coordinates. Doing so would likely reveal Waldo’s future locations much quicker than a basic technique (except in the case of outliers… which Olson later confirms there are several).
To find the optimal path (a solution to the traveling salesperson problem if you like), Olson used a genetic algorithm, which uses biologically inspired operators – such as mutation, crossover and selection – to continually improve its solution. In this case, the algorithm’s best solution is near-perfect, if not a little tricky to memorize and apply to every “Where’s Waldo?” image.
Thankfully, Olson has summarized some of the general lessons from the generated path. “The bottom of the left page is a good place to start,” Olson wrote in his blogpost. “If Waldo isn’t on the bottom half of the left page, then he’s probably not on the left page at all.”
The next spot to try is the upper quarter of the right page, failing that your next best bet is the bottom right half of the right page. If this still doesn’t reveal Waldo, then you’ve got a dreaded outlier, which may be hiding in the middle of the pages or the top left and right.
“When you're on an outlier illustration, you not only waste time following the path, but then you're left disoriented trying to trace back and worrying that you missed Waldo,” Olson wrote. “Waldo-spotting performance degrades on these outlier illustrations, so don't be discouraged by Book 1, which has 4 (!) outliers in it.”
For the rest, Olson said his method yielded a Waldo-find in less than 10 seconds; a mighty achievement but perhaps cuts short some of the potential enjoyment.
“This was all done in good humor and – barring a situation where someone puts a gun to your head and forces you to find Waldo faster than their colleague – I don’t recommend actually using this strategy for casual “Where’s Waldo?” reading,” Olson wrote. “As with so many things in life, the joy of finding Waldo is in the journey, not the destination.”
[H/T: Interesting Engineering]