From The University of Missouri Extension:
While some landowners still use the traditional “No Trespassing” signs, the Purple Paint Statute allows landowners to mark trees or posts with purple paint as a warning to would-be trespassers. Just like the “No Trespassing” sign or actual communication to individuals that no trespassing is allowed, the purple paint marks are considered to be adequate notice to the public that no trespassing is allowed on the property.
The purple paint law began in Arkansas in 1989 and Missouri enacted the same law during its legislative session in 1993. These statutes were enacted to provide landowners with an economical and easy way to keep out unwanted trespassers. The law does not require that property marked with the purple paint also be fenced, thus making it an economical alternative for landowners who do not otherwise need to fence their property. Additionally, it prevents problems encountered when using “No Trespassing” signs as purple paint marks can’t be taken down, destroyed, or even stolen.