The generalization of Sierpinski carpet and Sierpinski triangle in $n$-dimensional space

摘要

We obtain a nature generalization for an affine Sierpinski carpet andSierpinski triangle to $n$-dimensional space, by using the generations andcharacterizations of affinely-equivalent Sierpinski carpet. Exactly, in thispaper, a Menger sponge and Sierpinski simplex in $4$-dimensional space could bedrawn out clearly under an affine transformation. Furthermore, the method couldbe used to a much broader class in fractals.