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I have seen mountain lions and bobcats several times while living in the west, most commonly while out in the field, but sometimes while driving on a road or highway. Two encounters involved being very close to the animal in question while out doing some geologic mapping.
The first close encounter occurred on the east side of Shadow Mountain, a small group of low hills in northeastern San Bernardino County, north of I-15. Go to Baker, CA, the southern "Gateway to Death Valley," take I-15 east toward Vegas, go up the steep hill - on which many vehicles overheat and then have to be towed back into Baker, which makes a living by towing overheated vehicles - and then turn north at the Cima Road and Kingston-Excelsior-Mine-Road exit, which is where the old Stuckey's used to be. Then drive about 6.5 miles north on the Kingston Road, turn left on a major dirt road that parallels the Powerline Road, about 0.3 miles south of the powerline, and turn right after about 3.5 miles onto the Shadow Mountain Road, which is unmarked (I think). The first Google Earth image above shows Shadow Mountain, I-15, and the Mountain Pass Mine, a major producer of rare earth elements. The second image shows a view of Shadow Mountain from the south looking to the north, with the Kingston Range to the northwest and the Spring Mountains in the distance to the north.
Anyway, I was walking along an old road that was then inaccessible to 4WD traffic due to washouts. As I walked along, probably talking to myself about the middle Precambrian quartzite I was mapping, I approached an adit - an old tunnel driven westward into the side of the hill by oldtimer miners, possibly in the 1930's when a lot of prospectors and would-be prospectors took to the hills in southern California because there wasn't any work to be had. When I got to within about 50 feet of the adit, I heard a sudden rustling sound. I looked up, and a dark-colored, spotted-looking cat the size of a mountain lion rushed out of the tunnel, turned to look at me, and startled at least as much as I was, immediately ran down the road ahead of me as fast as possible.
Needless to say, I had some misgivings about continuing down the road. I finally walked down the road a ways, but then circled back away from the adit the cat had been sleeping in. Upon arriving back home after the 10-day trip was done, I looked up some types of cats, and came to the conclusion that the cat was either a young, spotted mountain lion (puma), or that it was possibly a jaguar from Mexico that was quite a ways north of its then known range. I didn't have a camera with me, and wouldn't have had time to take a picture if I had. The third Google image above, shows Shadow Mountain as viewed from the east, pointing out the adit in question. The Avawatz Range can be seen in the far distance to the west.
The second close encounter occurred in the Coast Ranges of California east of Hollister, in the Stayton Mining District, an old mercury district with some minor gold showings. The main workings of the district are all on private land behind locked gates. It was early spring and the grass was green, though not all the trees had leafed out. I had been mapping up above where I'd parked my truck, and the other geologists were off running some other traverses farther away from the truck. As I walked down the hill, I approached a road that went left toward my truck. Just below, I saw a strange-looking animal, which I first took to be a large Russian boar - they run wild in the Coast Ranges. I stopped walking and stood very still. I examined the nearby smallish trees as possible routes of escape in case the boar wanted to charge uphill.
The animal then came to a very small stream of water that was crossing the road. It stopped, batted at the water the way a cat will bat at a mouse, kind of playfully, and also distastefully because cats don't like water. At that moment, I realized the strange-looking animal was a cat - a funny looking one, but a cat nonetheless. I remained very still, hoping that it wouldn't see me. (All I had for defense was my rock hammer, which at the tine I didn't consider much of a defense - and I realized that the trees, if I had time to climb one, would be of no use to me whatsoever.) After batting at the water a couple times, the cat crossed the narrow streamlet and headed down the road, straight for the brushy, covered area where I'd parked the truck.
I stood there for awhile, not sure what to do, because the truck was my best defense, and the cat had just headed straight for it! After waiting awhile, I decided to go to the truck, essentially taking my chances. When I got there, I quickly threw my pack full of rock samples in the front, and climbed in as fast as possible. I backed out of there and drove up to meet the others. Later, when we left at the end of the day, we saw what may have been the same cat up in a tree, looking down on a bunch of deer.
I'm not sure why the cat looked so strange to me. It's possible it was a bobcat, but if so, it was probably a relatively large one. There really wasn't much in the area for size reference (for scale) except the width of the dirt road the cat was walking on. Maybe it was just walking strangely, maybe it's because I thought it was a boar to begin with. The cat we saw later in the tree was a full-sized mountain lion, with a definite tail.
Close enough for me!