When a gecko sticks itself to a wall, it's not sticking in the sense that there's some sort of glue-like adhesive helping it out. Instead, it's using the van der Waals force, which you may remember from high school as an attractive force between molecules themselves, caused by permanent or transient magnetic dipoles. These forces are very, very weak, which means that our friend the gecko needs to make contact with an awful lot of molecules all at once to get it to work, which is why the tips of its toes have the microscopic structures that you can see in the image above.
It's understandable why humans are trying to duplicate the ability of the gecko, and we've had some success at creating artificial gecko toes. The ones that we make look like this, from UC Berkeley:
The stuff that we've come up with works rather well, as long as it's got a nice flat surface to adhere to, like glass. It's what DARPA's Z-Man program is based on. But geckos can climb up all sorts of surfaces, flat and smooth or not, since they're animals with toes that can cling to things without having to rely on their adhesive properties completely. Humans haven't come up with a way to do this yet, but when we do, Spider-Man won't be much of a superhero anymore.
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