Where's Waldo? Algorithm Helps You Find Him
A computer program provides the optimal search path and ruins all of the fun.
Since 1986, the illustrations drawn by Martin Handford have been challenging readers of all ages with the question, Where's Wally? (Known as Waldo in the United States and Canada.)
Now a computer algorithm has plotted a path through the visual chaos, providing the fastest way to locate the iconic young man.
The algorithm was written by Randal Olson, doctoral student at Michigan State University. Olson writes on his blog that he was snowed in this past weekend and after coming across an old Slate article that claimed that it had a foolproof strategy for finding Waldo, Olson figured he could better it.
Thanks to a chart in the Slate article, Olson was able to plot Wally's locations from all 68 of Handford's books.
Next, Olson ran a kernel density estimation, which is a statistical method for estimating the probability density of a seemingly random occurrence. The kernel density looked like this.
Now he was getting somewhere. Next, he used that information to find an optimal search path across all illustrations that would put the reader in close proximity to all of Waldo's previously known locations.
Olson studies biologically inspired artificial intelligence and evolutionary processes, and so it should come as no surprise that he settled on a type of program called a genetic algorithm to find the optimal search path.
In Olson's words, "As you can see, genetic algorithms continually tinker with the solution - always trying something slightly different from the current best solution and keeping the better one - until they can't find a better solution any more."
The search path that came up is here.
Since the path is not perfect, Olson offers three tips for your next Waldo/Wally search.
Let us know how you do.
Credit: Randal S. Olson, William Murphy from Dublin, Ireland, Where's Wally World Record / Wikimedia Commons and "Martin Handford Wally & Friends"/ Wikimedia Commons
For years, opponents have argued that genetically engineered plants wreak havoc with human health and nature, and accuse plant biotech companies, such as Monsanto, of putting profits before people. On the other hand, agricultural biotech proponents argue that engineered crops enable farmers to grow at a time of global food shortages, insidious pests, weeds and extreme weather. "It's a complicated issue," says James E. McWilliams, author of American Pests and professor of history at Texas State University. Plant virologist Roger N. Beachy, president of the Donald Danforth Plant Center in St. Louis, Missouri, thinks that environmentalists and biotech experts can emerge from the cloud of controversy, find common ground, and move toward green goals together. So, whether transgenic crops make you think "yum-yum" or "no ma'am," McWilliams and Beachy share what's cooking:
1. Biofortified Soya Beans
What advantage did these few plants gain by evolving the ability to catch animals instead of just capturing the sun's energy? The elaborate structures necessary for killing bugs -- pools of nectar, bright colors, unusual shapes and digestive enzymes -- must be costly for the plant to make. Not so, says a new study, published in the American Journal of Botany, that examined Asian pitcher plants (pictured here), Venus flytraps, sundews and others.
2. Edible Cotton Seeds
By nature, cotton seeds are inedible because they contain gossypol, a component that keeps bugs away. In 2006, Texas A&M University and Cotton Inc. collaborated on research to produce genetically engineered seeds without the inedible part while keeping it in the plant for protection. The researchers made nutty-tasting meal from the seeds that could be used for flour, but the discovery has many regulatory and logistic hurdles to clear before it could be a reality in cotton-growing areas.
Food or energy? With gas prices soaring, biofuel advocates find themselves going toe-to-toe with farmers. Jatropha is an inedible plant whose seeds produce a liquid like palm oil that could be used for biofuel. Earlier this year the plant caused political tension in India, where tribal communities accused the government of destroying their native crops to plant jatropha for fuel needs. Plant breeding and genetic engineering will result in high-yielding jatropha that will increase overall production and potentially reduce the hectares needed; Roger Beachy says jatropha and other oil-producing, non-food plants also have the potential to produce bioplastics that can degrade in landfills.
4. Golden Rice
More than 120 million children globally don't get enough vitamin A and as a result are at risk for blindness. Back in the 1990s, a scientific team at the Swiss Federal Institute of Technology by Ingo Potrykis and collaborators at Syngenta Company discovered that adding several key genes from flowering plants to rice could dramatically increase the amount of beta carotene, a molecular that human beings can convert to Vitamin A. Even though the research ran into intellectual property rights problems, a public-private partnership between the inventors and agrichemical company Syngenta allowed the research to continue. Golden rice was successfully field-tested in Louisiana four years ago, but the inventors blame bureaucratic measures for slowing its adoption abroad.
5. Flood-Resistant Rice
Husband and wife team Pamela Ronald and Raoul Adamchak bridge the biotech-environmental divide in their book Tomorrow's Table, arguing that genetic-engineering and organic farming can be blended. Ronald, a professor of plant pathology at University of California-Davis, has been working with David Mackill of the International Rice Research Institute in the Philippines on genetically-modified rice that can withstand flooding. If field trials are successful, the rice could be available as early as next year.
6. Sugar Beets
For something that's so sweet, the debate over this crop has been rather bitter. Last year the New York Times chronicled sugar beet farmers' woes as they battled weeds to harvest the beets that provide around half the nation's sugar. They eagerly awaited Monsanto's Roundup Ready beets to produce higher yields and pay less for herbicide and workers to weed the fields. Environmentalists, meanwhile, raised alarm over the problem of weeds that are resistant to Roundup herbicide, cross-pollination with organic crops, and a group of advocates sued the U.S. Department of Agriculture over the matter. The beets became available to farmers earlier this year.
Admittedly, this isn't a crop, but it will likely be cultivated like one. The London Times recently reported that a biotechnology company in San Francisco called LS9 had genetically modified industrial yeast to munch on plant sugars and excrete crude oil. No, really. The company plans to feed the yeast agricultural waste, although they haven't quite scaled up the operation up beyond the beaker level. And there's no word yet on whether they will be able to engineer some bugs to eat up all the carbon dioxide from combustion.
This starchy, potato-like root is an essential plant for millions of people around the world, especially in Africa. This staple lacks a range of vitamins that are crucial to development and its cultivation can be adversely affected by drought. BioCassava Plus is a group of scientists led by Ohio State University Professor Richard Sayre and financed with a grant from the Bill and Melinda Gates Foundation. Currently they're working on a virus-resistant cassava that contains a day's worth of vitamins, proteins, and minerals. They plan to field test it in two African countries within the next two years.
Plant pathologist Dennis Gonsalves has been involved in papaya research for 30 years. It's not a stretch to say that papayas might have been wiped out entirely had it not been for his work. A virus was rapidly eating up the orange-yellow tropical fruit when Gonsalves, then at Cornell University, and fellow researchers engineered the SunUp papaya strain. Earlier this year, the University of Hawaii-Menoa led a group of 85 scientists to decode the SunUp papaya's genome -- the first fruit species sequenced. They'd like to use that information to strengthen the fruit's resistance to pests so farmers can cut back on the chemicals.
10. Castor Beans
"Plants make so many things," Roger Beachy says. He points to the castor plant, whose beans make versatile oil that can be used in a wide range of products, from jet engine lubricant to shampoo. The castor bean also contains a deadly toxin called ricin that has no antidote, which explains why the crop isn't very popular to grow. Two researchers at the U.S. Department of Agriculture became the first in the world to genetically engineer castor plants, blocking ricin production as well as intense allergens that the plants make. In addition, the USDA researchers would like to genetically engineer the plant to produce castor oil epoxy, which could replace toxic solvents in paints.