I've been following this thread for a couple of days and you guys are awesome! So many excellent ideas have been put forward as well as clever manipulations of the image, which I have no idea how to do.
I thought the logo looked kind of like the Quiksilver logo, but not exactly.
By the way, the Quiksilver logo is supposed to be a wave overtaking a mountain. The logo was designed by surfer Alan Green, the founder of Quiksilver. His drawing was inspired by the engraving by Japanese artist Katsushika Hokusai, “The Great Wave off Kanagawa.”
Like Gemmie, I thought the shape in the sole we're trying to identify looked more like a shamrock than the Quiksilver logo shape, which I guess is snow on a mountain. The sole we're trying to identify also looks more geometric than the curvier Quiksilver logo. Below is the Quiksilver logo that has been used from 1969 to today next to the shoe imprint we're trying to identify:
Starting in 2010, some Quiksilver products had this new logo:
The logo below has been used since 2010 too:
I found the history of these logos at this link:
The name and logo of Quicksilver symbolize the company's features - movement, speed, and the main qualities of the metal, reflecting the brand's philosophy.
logos-world.net
Unfortunately, there is no information about which Quiksilver products use which logo.
When Megs1477 posted the post below, I started looking at a lot of Quiksilver soles on flip flops, aided by RaspberryMama's and Megnut's hunches that these were flip flops. Quiksilver does have many products with the Quiksilver logo going in all different directions on the soles of their shoes. By the way, it's amazing how many variations on the logo and the Quiksilver name they have on the soles of their shoes.
Here is the sole of a pair of Quiksilver flip flops for boys:
You can see how the logo is all over the place, but it doesn't look exactly the same everywhere; the logos don't look like mirror images of each other. That lent credence to the idea that the sole we're trying to identify is like the soles above in which the logo and the Quiksilver name are similar, but not identical all over the sole.
So I finally found a sole that might possibly have that CA LADG kind of printing in it, but what do you think? This is the sole of a pair of Quiksilver Boys Molokai Black/Orange Flip Flops I found on Poshmark:
If you look in the middle of the tread of what would be the sole of the right shoe (the shoe on the left), can you see some lettering? Here is an enlargement of what I saw:
See how we have reverse vertical images of the logo that don't look like exact mirror images and to the right is what looks like a C with other letters following it? Can one of you that knows how to play with an image see if you can tell what the letters are? You can find the actual images at this link in case it's easier to play with the images from the original source:
Quiksilver Boys Molokai Black/Orange Flip Flops
If you guys think this shoe has some lettering like the sole we're trying to identify, the next question is, is this lettering in this shoe identical to what is in the unidentified sole? If not, maybe there is another style of Quiksilver flip flop with lettering identical to the supposed CA LADG in the unidentified sole.
I'm still looking at other soles to see if I can find others that appear to have lettering that begins with C. I've grown 10 years older since studying these soles.