& FractalDrawer Class $(45$ Points$)$

centuries because of their interesting mathematical properties and often appear in natural objects $($e$.$g$.$ snow flakes, plants$).$ Fractals are also a classic application of recursion; you can read more about fractals and their

history here. Consider the example below, which illustrates the process of constructing a fractal composed of triangles at several steps in the process. Notice that at each step, triangles of increasingly smaller sizes are drawn

at the three points of each existing triangle. More examples of fractals can be found at the end of this document.

Triangle fractal example

To help you with the drawing, we've already implemented a Canvas class that supports all of the drawing capability you need. You should look at the code if you're interested, but all you'll need to know is how you can interact

with Canvas objects.

Here are the method specifications of the Canvas class:

Canvas $()($defaulticonstructor$)$: Creates a canvas of default size $(800,$ pixels $*800$ pixels$)$

Canvas $($int height, int width$)$ : Creates a canvas of specified height and width.

$-$: void drawShape$($Circle circleObj$)$ : Draws the passed in Circle object.

$-.$ void drawShape$($Triangle triangleObj$)$ : Draws the passed in Triangle object.

void drawShape$($Rectangle Rectang leObj$)$ : Draws the passed in Rectangle object.

Each of the drawing methods will draw the shape you pass in$.$ This method accesses the color, position, and other attributes of the shape to draw it on the canvas.

Here's an example of how you might use the Canvas class to draw a single blue circle:

Canvas drawing $=$ new Canvas $(800,800)$;

Gircle myCircle $=$ new Circle $(0,0,100)$;

myCircle. setColor$(Color.$ BLUE$)$;

drawing.drawShape$(myCircle)$;

TI IMPORTANT: Java$($JFrame$)$ uses a coordinate system where the origin is in the upper lefthand corner. As cither the x and$/$or increases, the shape will move right and$/$or down. See the visual below.

Disual of Java$($JFrame$)$ coordinate system

You will be responsible for filling in the FractalDrawer class.

For full credit, your program should have the following features:

another$).$

IMPORTANT: The pattern must repeat on itself using recursion for full credit. Changing a shape's size or position should be involved in recursive calls.

Draw at least four shapes per layer for rectangles and circles and at least three per layer for triangles $($e$.$g$.$ draw the new shapes on all three points or sides of a triangle, or on four opposite sides of a circle $-$ again,