SEQUENCES, SERIES, FRACTALS, AND ART
BEFORE BEGINNING THIS PROJECT, PLEASE WATCH THIS SHORT VIDEO
ON FRACTALS: http://www.youtube.com/watch?v=XwWyTts06tU
On Friday, we spoke of many ways to create art out of sequences. You have the
opportunity to create your own art project for extra credit. The project is worth 10 quiz
points.
Each project must include:
1) An piece of art created by yourself (must be at least 1/2 poster board In size)
Follow the instructions for the project to create a visual representation of a sequence/series.
Sketch out rough drafts to make sure you’re on the right track. Once you are ready, take
your time in creating a final product that incorporates color and creativity. While I do not
expect all of you to be supreme artists, your product will be graded on accuracy and
execution. Please create a product that you are proud of and will enjoy showing the class.
2) A mathematical write up
Answer the follow-up questions for your project. It may be helpful to read through the
questions prior to starting your drawing and/or fill out the table as you go. You may work
with others to check your answers, but you are all responsible for turning your math in with
your project. If you run out of room on the sheet provided, you may continue on notebook
paper.
(Please note, the write up asks for certain calculations. Your picture/art work does not need
to follow those measurements. However, your picture should match your write-up. So, if
you choose to draw the Sierpenski’s triangle, you must do the write-up for Sierpenski’s).
Note: You may also choose to explore patterns/sequences/series/fractals that are not
listed in this packet. If you choose a different project, you will need to show adequate
amount of math (e.g. a table and recursive formula(s) for a property of your drawing).
****I HAVE INCLUDED A NUMBER OF LINKS ON THE LAST PAGE TO HELP
YOU WITH IDEAS AS YOU BEGIN YOUR PROJECT. PLEASE BE SURE TO
REVIEW THE LINKS FOR THE TYPE OF PROJECT YOU WILL COMPLETE.
GRADING RUBRIC:
POINTS:
1-2
Heading
(1 POINT
ONLY)
3
4
An attempt was made,
however, It was sloppy
or incomplete.
Art piece shows at least
5 levels of the
sequence.
Art piece shows at least
5 levels of the
sequence.
Color was not used
and/or project did not
show precision in
drawing.
Size of project is at
least ½ standard poster
board (can be larger if
desired).
Size of project is at
least ½ standard poster
board (can be larger if
desired).
Student did not include
a minimum of 5 levels
of the sequence.
Some effort was made
to color the project.
Student has shown
precision in drawing
accurate sequences.
Student has name, class
hour, and name of
project on back of art
work.
Write up is pasted to
the back of the project
as well.
Art
Math
Write up is incomplete,
but attempted
TOTAL POINTS EARNED:
Parts of the project may
be messy or sloppy, but
Student used their
overall an effort was
creativity to make
made.
colorful and interesting.
Effort is evident in
artwork.
Write up is complete,
Write up is complete
but only partially
and correct.
correct.
If student has used their
own sequence, they
have included the
recursive formula and
table. They have
explain why they chose
their particular
sequence.
YOUR
SCORE
GET YOUR MIND GOING BY LOOKING AT THESE WEBSITES:
FRACTALS:
http://www.youtube.com/watch?v=XwWyTts06tU
http://fractalfoundation.org/resources/what-are-fractals/
http://fractalfoundation.org/fractivities/WhatIsaFractal-1pager.pdf
FIBONACCI SEQUENCE
http://www.youtube.com/watch?v=ahXIMUkSXX0&feature=youtu.be
(….doodling flowers http://www.youtube.com/watch?v=lOIP_Z_-0Hs&feature=youtu.be )
http://www.ldlewis.com/Teaching-Mathematics-with-Art/golden-ratio-instructions.html
http://mathworld.wolfram.com/FibonacciNumber.html
Fibonacci in Music: http://www.youtube.com/watch?v=pOwMDO0-zBw
SIERPINSKI’S TRIANGLE
http://www.youtube.com/watch?v=Yhlv5Aeuo_k
http://rocketmandevelopment.com/static/media/uploads/2010/06/Sierpinski-triangle.png
NESTED SQUARES:
http://fineartamerica.com/featured/colorful-nested-squares-bonnie-bruno.html
http://fractalwise.deviantart.com/art/Spirograph-Nested-Squares-152626091
VON KOCH SNOWFLAKE
http://www.math.ubc.ca/~cass/courses/m308/projects/fung/page.html
DRAGON CURVE FRACTAL:
http://www.youtube.com/watch?v=BdaOwIHK5cc
OTHER SERIES
http://mathworld.wolfram.com/SternsDiatomicSeries.html
Circle wall painting: http://www.youtube.com/watch?v=qTB2lUI5sAo