  The paper describes a new algorithm of construction of the nonlinear
arithmetic triangle on the basis of numerical simulation and the binary system.
It demonstrates that the numbers that fill the nonlinear arithmetic triangle
may be binomial coefficients of a new type. An analogy has been drawn with the
binomial coefficients calculated with the use of the Pascal triangle. The paper
provides a geometrical interpretation of binomials of different types in
considering the branching systems of rays. Results of numerical calculations of
binomial distribution of the second (nonlinear) type for big power of a
binomial are given. Difference of geometrical properties of linear and
nonlinear arithmetic triangles and envelopes of binomial distributions of the
first and second types is drawn. The empirical formula for half-sums of
binomial coefficients of the second (nonlinear) type is offered. Comparison of
envelopes of binomial coefficients sums is carried out. It is shown that at big
degrees of a binomial a form of envelops of these sums are close.
