To Collection-loving Simmers.
I rarely go to Destination World, but since there is a rule that I was able to confirm in a part of Home World, I will list it here for reference.
1. When you visit the area for the first time, rocks and fallen frog trees will appear within a few hours.
2. After the second time, it will start appearing from around 1:00 A.M., so if you are in that place at that time, you can collect it.
3. The frog well in Oasis Springs cannot be harvested every day while in the area. Even if you live in it, if you move to another area, you can collect it when you come back.
(The well near Slipshod Mesquite (Zest's house) in the Bedrock Strait area, near the grill and vegetable garden, and the well next to Greg's house in Moonwood Mill will not spawn frogs after the second time.)
The above is confirmed in the three base game worlds, Windenburg, Moonwood Mill, Forgotten Hollow, and Sulani.
In Britechester and the Galloping Gulch area of Chestnut Ridge, rocks and fallen frog tree will already spawn when you move to another area and come back. In If you lived in Britechester, the rocks didn't spawn unless you moved to another area.
By the way, 15 types are written in the achievement, but if you will complete 13 types of the base game (Frog, Gardening, My Sims Tropheies, Metals, Crystals, Elements, Postcards, Fossils, Microscope Prints, Space Prints, Aliens, Space Rocks, Fish), you can get the "For The Hoard" Achievement.
Good luck.
