The system is simple. A ding (a dot) counts as 1. But anything inside a ring (a circle) is doubled. A ding inside two rings is doubled and doubled again. Here's the numeral for 13:
The rings must be nested. The innermost ring must have a ding. No region can have more than one ding. Those are the only rules.
View a few numbers of your choosing at
The fun comes when you add and multiply numerals. To add two numerals, you put them together and watch. They will put on show getting together. I won't spoil the show by describing it.
You can see numerals (of your choosing) doing addition in real time if you go to
Multiplication is even more exciting. To multiply one numeral by another, you simply replace each ding in one numeral with a copy of the other numeral. Then as before the rings and dings will then sort themselves out. It's a quite a show.
You can watch numerals (your choice!) do their stuff at
Special thanks to Fred Henle for technical assistance, tasteful suggestions, and timely encouragement!