Applied Math 40S

Draw the following fractals. Be sure to save your drawings and bring them to class tomorrow. Draw them centered, one fractal per page.

(1) Draw a rectangle that measures 12 cm by 8 cm, and shade the inside of the rectangle. Construct the midpoints of each side of the rectangle, and then draw a quadrilateral by joining these points. Shade the quadrilateral white. Now continue the process by finding the midpoints of the quadrilateral, drawing the rectangle, and shading it the same colour as the first rectangle. Draw six generations. (The initial rectangle is the first generation.)


(2) Create a fractal that begins with a large square 20 cm on each side. Each pattern requires that the square be divided into four equally sized squares, that the bottom-left square be shaded, and the process continues in the upper-right square. Repeat the process four times.


(3) Create a fractal where a square is inscribed in a circle. The diameter of the original circle is 16 cm. Shade the area between the circle and the square. Inscribe a circle inside the resulting square, and then inscribe a new square inside that circle, and shade the area between the new circle and square. Repeat this process three times.