Fractals Homework Fractals Homework Due Wednesday by 11:59pm Points 100 Submitting a file upload File Types pdf Submit Assignment Complete the following activities: 1. The first two iterations of a...

please do all questions


Fractals Homework Fractals Homework Due Wednesday by 11:59pm Points 100 Submitting a file upload File Types pdf Submit Assignment Complete the following activities: 1. The first two iterations of a fractal tree are given below. Sketch what the third iteration will look like. Information that you will need for the sketch: the new segments are 1/3 the length of the old segments. The segment to the left attaches at a angle and the segment to the right attaches at a angle. You can sketch the third iteration by hand or you can use the link to open the fractal in Geogebra and use that to draw the third iteration on the partially pre-built one ready for you there. In Geogebra you can use any tools available to you including the create angle with measure tool and the create segment with length tool or create circle with radius tool (the circle tool is easier to use for this if you ask me). If you draw it by hand, scan or take a picture of your completed creation and paste the picture in your homework document. If you use Geogebra then export your finished creation as a picture and paste in your homework document. Link to Geogebra file: https://www.geogebra.org/geometry/xavcqeub (https://www.geogebra.org/geometry/xavcqeub) 2. Below are the first two iterations of a fractal related to the Koch Stool discussed in your lesson material. It is created by removing the middle two fourths of a line segment and replacing the first fourth with a square going "up" from the segment and the second fourth with a square going "down" so each new line segment is 1/4 as long as the old one. For further iterations you do this again with all line segments of the old iteration. Describe a similarity transformation that would map this fractal onto a smaller part of itself. You do not have to give an explicit formula here, just describe any rotations, translations, and scaling needed. 3. Compute the fractal dimension of the line fractal in activity 2 using the formula from the lesson material. 4. The first two iterations of a fractal shape called the Menger Gasket are given below with an image of what the complete fractal would look like below that. The Menger Gasket starts with a filled in square and then follows the instructions 1. Split the square into 9 smaller squares (by splitting the sides into thirds). 2. Remove the square in the middle. 3. Repeat these steps with the 8 small squares that are left. Sketch what the third iteration of the Menger Sponge will look like. You can sketch the third iteration by hand or you can use the link to open the fractal in Geogebra and use that to draw the third iteration on the partially pre-built one ready for you there. In Geogebra you can use any tools available to you. (Here's a hint: In Geogebra if you are clever you can construct only one smaller square and use a specific tool combination to make all of the other you will need!). If you draw it by hand, scan or take a picture of your completed creation and paste the picture in your homework document. If you use Geogebra then export your finished creation as a picture and paste in your homework document. Remember that to make a filled in square in Geogebra you use the polygon tool to make the square and then open the settings for the polygon, go to the color tab, select the color you want, and then set the opacity slider to 100. Link to Geogebra file: https://www.geogebra.org/geometry/fe8nejfz (https://www.geogebra.org/geometry/fe8nejfz) 5. Now that you have used instructions to create a few fractals like the tree, line fractal, and shape fractal above, make your own instructions and draw the first two iterations of your fractal following them. You can draw the fractal by hand or using Geogebra. Save your fractal as a picture and paste it into your homework document 6. Use the complex fractal generator discussed in the lesson that is found at http://usefuljs.net/fractals/ (http://usefuljs.net/fractals/) to get an image of a piece of a complex fractal that you think looks nice. You can generate your own fractal by adjusting the constants in one of the Julia Fractal generators or you can find a zoom that you like on one of the fractals that you can't change constants on. Once you have an image you like, share it on the discussion board "My Favorite Fractal". In your discussion post, tell what you did to get the image (i.e. "I zoomed in on this area of the Mandelbrot" or "I set the Quadratic Julia constant to...") and what you liked about it. Feel free to comment on other students fractals (kindly!) but I'm not going to require it this time.