Pattern in the Chinese numbers 1 to 9
一二三 should be self-evident, they are equivalent to Roman numerals, that is, simple enumeration symbols.

Then it gets murky, but note that even numbers 二四六八十 are all symmetrical, whereas the odd numbers (一三)五七九 are not.

四 is defined by this symmetric property, as an even number that can be halved. 六 is actually a 四 with a dot above, using old seal script. 八 is also defined as a mirror symmetry, indicating divisibiliy.

As for 五七九, there are no good etymological derivations, they are simply symbols since long lost in origin. There are no patterns associated with these characters.