Animated Sierpinski Carpet

The sierpinsky carpet is a self similar plane fractal structure.

Animated sierpinski carpet.

Animated sierpinski carpet by karocksorkav own work. Sierpinski carpet generator tool what is a sierpinski carpet generator. Divide it into nine squares 3 3 and remove the center one. Animated construction of a sierpinski triangle playback x 4 mathematics proofs gcse a level.

It s an animation of different iterations of sierpinski s carpet. 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. 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.

Plotting a sierpinski carpet fractal. How many stickers will need in each iteration. Licensed under cc by sa 3 0 via wikimedia commons. A very challenging extension is to ask students to find the perimeter of each figure in the task.

The sierpinski carpet is the intersection of all the sets in this sequence that is the set of points that remain after this construction is repeated infinitely often. This produces a geometrical object with a gap of zero area but with infinite perimeter. To construct it you cut it into 9 equal sized smaller squares and remove the central smaller square from all squares. This tool draws a sierpinsky carpet.

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. To generate the carpet take a square. Note that the perimeter includes the lengths of the edges of the holes that. 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.

The figures below show the first four iterations. The squares in red denote some of the smaller congruent squares used in the construction. Sierpinski carpet duration. Movie vertigo 1 953 views.