We continue to study harmonic functions on Sierpinski gasket and finally introduce what I call "non-commutative number system". In such a system to a string $a_1a_2\dots a_n\dots$ where $a_i$ are "digits" taking values in a finite set (usually {0,1} or {1, \epsilon, \bar{\epsilon}) we associate a number $v^*\prod_{k=1}^\infty M_{a_i}v$. Here $v$ is a column n-vector, $v^*$ is a row n-vector and $M_k$ are $n\times n$-matrices. It turns out that this generalization of ordinary $M$-adic system allows to write the simple formula for some remarkable functions arising in the study of some fractals.