How to use sed / awk / grep … to extract blocks from a file and each block save it into a file

How to use sed / awk / grep … to extract blocks from a file and each block
save it into a file

Good day to all,
In this opportunity, I'm trying to find a bash code that allow me to
extract text blocks between the same pattern and each block save to a
different file.
My first approach is:
sed -n "/PATTERN/,/PATTERN/p" file.log
{...and yes, into the log file, the pattern that delimit each block is the
same}
But it only print all blocks in one stream... I want to save each block
into a file. But, I don't know how to make a stop in each block, save it
and continue with the following block.
Thanks so much in advance for any help.
`
PATTERN
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut
wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit
lobortis nisl ut aliquip ex ea commodo consequat.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut
wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit
lobortis nisl ut aliquip ex ea commodo consequat.
PATTERN
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut
wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit
lobortis nisl ut aliquip ex ea commodo consequat.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut
wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit
lobortis nisl ut aliquip ex ea commodo consequat.
PATTERN
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut
wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit
lobortis nisl ut aliquip ex ea commodo consequat.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut
wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit
lobortis nisl ut aliquip ex ea commodo consequat.
`