Animated Sierpinski Carpet

Divide it into nine squares 3 3 and remove the center one.

Animated sierpinski carpet.

A very challenging extension is to ask students to find the perimeter of each figure in the task. To construct it you cut it into 9 equal sized smaller squares and remove the central smaller square from all squares. This produces a geometrical object with a gap of zero area but with infinite perimeter. The sierpinski carpet is a compact subset of the plane with lebesgue covering dimension 1 and every subset of the plane with these properties is homeomorphic to some subset of the sierpiński carpet.

The squares in red denote some of the smaller congruent squares used in the construction. Versions 2 and 3 plotscf gp and plotscf1 gp file functions for the load command are the only possible imitation of the fine functions in the gnuplot. Sierpinski carpet generator tool what is a sierpinski carpet generator. Movie vertigo 1 953 views.

The sierpinsky carpet is a self similar plane fractal structure. The figures below show the first four iterations. Animated sierpinski carpet by karocksorkav own work. 7 iterations of the carpet.

Animated construction of a sierpinski triangle playback x 4 mathematics proofs gcse a level. How many stickers will need in each iteration. You can simplify the code and make it run faster if you construct the next level carpet by continuing to work on the previous image punching more holes in it rather than starting with a blank slate every time. Then for each of the remaining 8 squares repeat ad infinitum.

Plotting a sierpinski carpet fractal. The figures students are generating at each step are the figures whose limit is called sierpinski s carpet this is a fractal whose area is 0 and perimeter is infinite. Licensed under cc by sa 3 0 via wikimedia commons. Sierpinski carpet duration.

It s an animation of different iterations of sierpinski s carpet. This tool draws a sierpinsky carpet. Animated sierpinski carpet by karocksorkav in each iteration the number of squares is multiplied by 8 and instead the same side is 1 3 of the above. Note that the perimeter includes the lengths of the edges of the holes that.