Question

Case Study 3: Sierpinski Triangle A fractal is a geometric object that is self-similar. That is, if you zoom in on the object, it retains the same appearance or structure. One such fractal is the Sierpinski Triangle which is formed by drawinga triangle and removing an internal triangle drawn by connecting the midpoints of the outer triangle's sides. This process is repeated recursively ad infinitum. This process is illustrated for the first four iterations in the figure below. Figure 1Sierpinski Triangle, 4 iterations A Java applet has been provided to you (unl.cse.recursion.SierpinskiTriangle) that recursively draws the Sierpinski Triangle for a specified number of recursive iterations. Since this is an applet, you can run it without having a main method. The depth of the recursion is specified in the paint method. It will be your task to modify this program to count the total number of triangles that a recursion of depth n will ultimately render.

Answer 1

int countTriangles(int depth) {
    if(depth == 0) {
        // 0 depth has only one triangle
        return 1;
    } else {
        // 1 Single triangle, results in 4 triangle
        // Out of those 4 triangles, the corner 3
        // triangles are
        // recursively broke into other triangles.
        return 1 + 3 * countTriangles(depth - 1);
    }
}

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