*A while back I created animations with music generated by mathematical number sequence.  I had not explained the method yet. So it is a perfect topic for another post :D*

A number sequence is just an ordered set of numbers. For example, { 1 , 2 , 3 , 4 ,  5 , 6 } is a sequence.  These sequence can also have infinite elements. For example, you can convert π to a sequence by ordering its decimals in the natural way, so like this { 3 , 1  , 4 , 1 , 5 , 9 , ... }.   You can also use a function to generate a sequence. For example, the sequence generated by  n<sup>2</sup> for n=1 to n=3 is given by {1 , 4 ,  9}.

Here are two  videos I generated using number sequences:

<center>
<a href="https://d.tube/#!/v/mathowl/ft7tj4gm" rel="noopener" title="This link will take you away from steemit.com"><img src="https://steemitimages.com/0x0/https://ipfs.io/ipfs/QmYtimX3GNXTDVgjFiPzQWK1XarBxZVYkjaV9fbzAd9hmH"></a><div></div><div></div>
</center>

<center>
<a href="https://d.tube/#!/v/mathowl/tkfji0fh" rel="noopener" title="This link will take you away from steemit.com"><img src="https://steemitimages.com/0x0/https://ipfs.io/ipfs/QmbUgLwTp7HhG9EmXfwpmjLeNYEqBHb56weh9ciE6jrzi2"></a>
</center>

There is the animation and there is the piano music. The main idea is that the sequence is converted to animation frames and the animation frames are then converted to piano music. So I will kick off with explaining how the animation is generated.


<div class="pull-right"><img src="https://cdn.steemitimages.com/1400x1400/https://cdn.steemitimages.com/DQmTQHPLYoZKsprUGWP9rv9Rpk43dmavvLvx5W4epgpT4gv/dancinglines.png" /></div>

## Animation
Let me explain the animation method by example. Consider the sequence { 1 , 2 , 3 , 4 ,  5 , 6 } . This sequence will act like a list of sequential commands which describe a road/path. We need to start by selecting a point on a white sheet of paper, see the black dot in the image on the right. The first number of the sequence indicates the distance we need to move in a west-ward direction.  For the considered sequence the distance is 1. Then we make a 90 degrees angle towards the left and go forward in a distance equal to the second number, which in this case is 2.  Then we  make a left 90 degrees angle and go forward in a distance equal to the third number, which  in this case is 3.  Then we make... you get the idea, we just repeat the process. The path traced will then be given by the image on the right.



<div class="pull-left"><img src="https://cdn.steemitimages.com/DQmV5GT7pFbD1ooXkCs6hfhRB74TXzXYg9EJoE7vUq6r1xV/dancinglines.png" /></div>

## Music
I will continue with the same example, the sequence { 1 , 2 , 3 , 4 ,  5 , 6 } .  The position of each 90 degrees corner on this winding figure, the red dots in the image, can we represented in the plane by an x- and y-coordinate. The x- and y-coordinate  can then be mapped onto the keys of a piano. More specifically, I will let (x,y) correspond to a musical interval using the method of one of my [previous posts](https://steemit.com/mathematics/@mathowl/math-art-5-the-sound-of-integer-sequences). When the program draws an edge it will simultaneously play that interval. 



## Back to the videos
Now that we know how the videos were generated we can have a look at what kind of information we can derive from the videos. For the first video we see that it seems to converge to a square so this means that all edge have the same length so  the final numbers of the sequence are all the same. The second video, the decimals of √2, described an irratic pattern. This makes sense because  √2 is an irrational number, so when you write the decimals as a sequence the sequence never repeats itself. That is why you get the strange pattern. :D


 





<hr>

**Sources:** All images made using [inkscape](https://inkscape.org/en/) it is free!
<hr />
<center>
<h2> Merchandise :D </h2><br />
</center>
<p><img src="https://steemitimages.com/0x0/https://cdn.steemitimages.com/DQmdwbunfcePxAncstQN21fDefS97B3ofRrAABmi29zD26B/g7592-1-9.png" alt="2018-06-07 (2).png" /><br />
There is a  <a href="https://www.redbubble.com/people/MathOwl/shop" rel="noopener" title="This link will take you away from steemit.com">MathOwl shop</a> which sells my artsy fartsy stuff. If you got some spare money head over there. You can learn about the colors of pi over here <a href="https://steemit.com/mathematics/@mathowl/math-art-4-the-colors-of-p">here</a>.  I also have really cheap stuff available like these <a href="https://www.redbubble.com/people/mathowl/shop/stickers?accordion=product&amp;cat_context=u-stationery&amp;ref=artist_shop_product_refinement&amp;asc=u" rel="noopener" title="This link will take you away from steemit.com">stickers</a> They are an absolute hoot.</p>
<hr /> 
<hr /> 
<p></p><h3><center>Join <a href="/trending/steemstem"> #steemSTEM</a></center></h3>
<p><a href="/trending/steemstem">#steemSTEM</a> is a community project with the goal to promote and support Science, Technology, Engineering and Mathematics related content and activities on the STEEM blockchain. If you wish to support the <a href="/trending/steemstem"> #steemSTEM</a> project you can: <strong>Contribute STEM content using the <a href="/trending/steemstem"> #steemstem</a> tag | Support steemstem authors | Join our curation trail | Join our <a href="https://discord.gg/mKSKQ7T" rel="noopener" title="This link will take you away from steemit.com">Discord community</a> | Delegate SP to steemstem</strong></p>
<h4><center>Convenient Delegation Links:</center></h4>
<p><strong><center> <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=101913.0159%20VESTS" rel="noopener" title="This link will take you away from steemit.com">50 SP</a> | <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=203826.0318%20VESTS" rel="noopener" title="This link will take you away from steemit.com">100SP</a> | <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=1019130.1592%20VESTS" rel="noopener" title="This link will take you away from steemit.com">500SP</a> | <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=2038258.3074%20VESTS" rel="noopener" title="This link will take you away from steemit.com">1000SP</a> | <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=10191291.5921%20VESTS" rel="noopener" title="This link will take you away from steemit.com">5000SP</a> | <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=20382581.1841%20VESTS" rel="noopener" title="This link will take you away from steemit.com">10000SP</a> | <a href="https://steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=steemstem&amp;vesting_shares=101912901.9206%20VESTS" rel="noopener" title="This link will take you away from steemit.com">50000SP</a> </center></strong><br />
<center><img src="https://steemitimages.com/0x0/https://cdn.steemitimages.com/DQmYSEjNhZDkm4FQPsnPgBdLszb82txzj4fNtKh2Bhb5uiU/banner.png" /></center><center>Image courtesy: <a href="https://steemit.com/@mathowl">Me ;) </a></center>