How to draw a Sierpiński carpet with a geometrical drawing board

Analysis: Take the square 9 equal, get 9 small squares, give away the central small square, keep around 8 small squares. Then 9 equal parts for each small square, and likewise the central square. According to this rule constantly subdivided and shed, until infinity. The limit graph area of Sierpiński carpet tends to zero, the number of small square and its side line is more and more infinite, it is a line set, and the graph has strict self-similarity.

The specific drawing steps are as follows:

1. Open the geometry of the artboard software, on the plane arbitrarily draw line AB, to segment AB for the edge of the long structure square ABCD.

Construction of square ABCD with segment AB as side length

2. With point A as the Zoom center, the point B, D is scaled to 1/3 to get E, F, and D to zoom Center, the point A, c scaling to 1/3 to get G, H. Get the same point I, J, K, L. Connect the points and divide the squares into nine halves.

Square ABCD nine equal parts by scaling

3. Click on "Data-new parameter" New parameter n, the value is changed to 2. Click a, b two points in turn (note: These two points are the two endpoints of the segment you first drew) and parameter n, hold down the SHIFT key and click "Transform-depth iteration" To open the iteration dialog, select G, p Two, click "Structure"-"Add a new map", select P, o two, and continue adding new mappings. Select O, J; F, M; N, K; A, E; E, L; L, B. (Note: The middle of the M, n two points do not point) click "Iteration", complete the iteration production.

Perform depth iterations on points of squares

4. Fill in the middle square mnop, measure the area of the MNOP, select the measurement result and fill the square, click "Show"--"color"--"Parameters", click "OK" in the pop-up dialog box.

Fill square Mnop and set color parameters

5. Finally, select all points and press Ctrl+h to hide unnecessary points.

Hide a little finished Sierpiński carpet making

Warm tip: Change the size of the square ABCD, the color of the square mnop changes with its area. The difference of Sierpiński carpet is observed by changing the value of parameter N.

Change parameter n to observe the difference of Sierpiński carpet