Here we are going to study Sierpinski-like Gaskets made from Pascal-like triangles.
We let p = 3 and v = 1, and make a triangle by U(p,n,m,v) for natural numbers n,m with n≤7 and m≤n. Then we get the following Figure 3.
If we calculate each U(p,n,m,v), then we get the following Figure 4.
If we calculate the least nonnegative residues of numbers in Figure 4 taken modulo 2, then we get the following Figure 5.
In the 20th century Professor Waclaw Sierpinski discovered the Sierpinski Gaskets.
In the 21th century the authors discovered Sierpinski-like Gaskets.
When authors discovered this gasket, they did not know the original Sierpinski Gasket, and the teacher was very surprised!
This Sierpinski like Gaskets can make a beautiful movie.
See the movie in the Gallery.
The above is a Sierpinski-like gaskets. If we express numbers with different colors, then we get a beautiful triangle.
If you add more rows, the triangle becomes more beautiful.
3. Sierpinski like Gaskets made from Pascal like triangles.
Figure(3)
Figure(4)
Figure(5)
If we make gaskets for different natural number p, and by using these gaskets we can make a movie.
In this movie the picture is very similar to Sierpinski Gasket, but gradually the difference becomes bigger.
Sierpinski-like gaskets is very different from Sierpinski Gasket in one point.
Some mathematicians are interested in these Sierpinski-like gaskets from the point of cellular automaton.
Sierpinski-like gaskets have a kind of boundary condition to produce numbers.
