What is this?
The spider in your photo is a tan jumping spider, scientific name: Platycryptus undatus, in the family Salticidae. As their name implies, jumping spiders are heavy-bodied, short-legged spiders that are capable of jumping. They do not spin webs to capture prey, rather they wander around on foliage, bark, or the walls of buildings searching for prey items. Their front pair of eyes are greatly enlarged and they have excellent vision for a spider. This is why the spider was darting around whenever you moved. It was seeing you moving and was positioning itself to get a better view of you in case it sensed you might be a threat and it needed to escape. The tan jumping spider is one of the largest of the hundreds of species of jumping spiders that occur in the U.S. Jumping spiders, are very docile, rarely bite and basically harmless to humans. I have included some links below to websites with more information about jumping spiders.
Thank you for replying. I'm so glad that I didn't kill it, I already lived with brown recluses for years and I just deemed that spider worthy to live because I thought that it looked awesome and I have never seen one of those before.