Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

Fractals and Sequences

No description
by

Jennifer Preissel

on 18 December 2015

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of Fractals and Sequences

Sequences and Fractals
They are all repeating visual
patterns
, called
fractals
...
Your Task:
Investigate a fractal. Determine which mathematical equations generate the patterns (or
sequences
) occurring in the fractal.

First. Some review. Remember that
arithmetic

sequences
are generated by the repeated addition of a
common difference
.
Some examples:
2, 4, 6, 8, 10...
10, 5, 0, -5, -10....


Geometric sequences
are generated by the repeated multiplication of a
common ratio
. Some examples:
2, 4, 8, 16, 32....
1, 3, 9, 27, 81...
-1, 1, -1, 1, -1...
4, 2, 1, 1/2. 1/4, 1/8...
And
recursive sequences
are generated by repeatedly applying the same pattern to each term to arrive at the subsequent term. The most famous example of this is the
Fibonnacci sequence
, whose formula is as follows:
t(0) = 1, t(1)=1
t(n+1) = t(n) + t(n-1)
1, 1, 2, 3, 5, 8, 13, 21...
Visit these links for more resources on fractals...

See what art you can create from fractals:
https://professortiz.wordpress.com/2013/07/22/geogebra-art/#jp-carousel-636

Play with this fractal machine to generate your own fractals: http://sciencevsmagic.net/fractal/#0103,0495,2,2,0,1,2

Learn about the fractal nature of rivers: http://fractalfoundation.org/resources/fractivities/fractal-rivers/

Here are some more "Fractivities" you can do on your own: http://fractalfoundation.org/resources/fractivities/

Now it's time for you to see how sequence equations relate to fractal patterns.

We are going to investigate a fractal called the Serpinski's Triangle, which you can see below.









Run several stages of the activity here:
http://www.shodor.org/interactivate/activities/SierpinskiTriangle/

Answer related questions in the Google form here:
http://goo.gl/forms/vxts5fvpmj
What do this shell...
...the Grand Canyon...
...Romanesco broccoli...
...a flash of lightning...
...and the Milky Way
galaxy have in common?


What makes a fractal a fractal?
Click here to find out more:

https://georgemdallas.wordpress.com/2014/05/02/what-are-fractals-and-why-should-i-care/

Visit the link here to add your thoughts to the discussion: http://ed.ted.com/on/PJCeHRda/discussions/seeing-patterns

The Fibonnaci Sequence occurs frequently in nature. Flower petals and spirals (like seashells) replicate outwardly in this pattern. Watch this video to find out more about how nature relis on this pattern.
Visit the
quiz
here to pratice your application of these concepts:
http://ed.ted.com/on/PJCeHRda#review
(Remember to log in to your TedEd account to participate in the conversation.)
Fractals can be harnessed for technological uses as well. Watch the above primer on fractals to learn about a real world application that you probably rely on every day.
Let's examine the Nested Square fractal in order to determine which sequence equations generate its patterns: http://tube.geogebra.org/material/simple/id/323697






Answer related questions in the Google form here:
http://goo.gl/forms/vxts5fvpmj
Full transcript