Welcome to Bladeforums goldenpie6.
For starters, it is perfectly legal to possess "gravity" and "butterfly" knives in the state of California and keep them at home. You may already know that in order to carry such knives in public, or possess them in the driver/passenger area of a motor vehicle, that they need to have blades under 2" long.
Here is a list of the bladed items that are illegal to possess under any circumstances under California law (some are a bit strange)-
Air gauge knife (a knife designed to look like a tire pressure gauge)
Ballistic knife (any device that shoots a knife blade)
Belt buckle knife (but only illegal if the blade is 2.5" or longer. shorter than 2.5" is legal to own)
Cane sword.
Lipstick case knife (a knife designed to look like a tube of lipstick)
Shobi-zue (a martial arts type weapon with a blade hidden in a "staff, crutch, stick, rod, or pole" that is deployed by a flick of the wrist or mechanical action)
Writing pen knife (a knife designed to look like a pen)
Shuriken (throwing stars)
I got all of the information for this list from the official California state legislative website, which can be found here-
https://www.leginfo.legislature.ca.gov/faces/home.xhtml
To search that site for knife laws, click on "California Law" in the banner under the site logo, then click "Text Search" (middle of the page on the left, next to "Code Search"), then use the search function to search for any word or subject you like (you'll need to click "PEN" at the bottom of the middle column to conduct your search. "PEN" for penal code).