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*by Javantea*

*July 28, 2015*

**Update July 29, 2015**

**Javantea**

@Javantea

My research into polynomials has led to a 3x3 captcha solver today. It's very fast. My next attempt will be a 6x6 captcha solver.

4:39 PM - 29 Jul 2015
Rather than discuss something important or release something interesting, I thought I'd release a piece of non-music audio for the purpose of demonstrating a new breakthrough I've made in sample production and artificial intelligence research. I have automated the process of creating samples based on polynomials. It's a very streamlined process which has produced the below samples. They aren't meant to be musical, so don't complain. Also their **volume is way too high** so you should turn down your volume before listening to them.

Each are 6 minutes long and it's pretty obvious what the theme is. It doesn't change drastically. That's because it's not music. What is shows is a simple algorithm.

- Take a polynomial, in the case of Unfortunate 3 it's
f(x) = A*x

^{2}+ B*x + C - Pick the coefficients to fit a specific set of x, y values.
- Append the values [int(f(i)) for i in range(1024)] to the audio.
- Change the curve y values.
- Goto 2.

This is a very efficient algorithm which can produce a very large set of functions. How large? Let's plot 50 random polynomials out of the 15625 that make up Unfortunate 3.

Unfortunate 3 uses the simplest polynomial that I dare use for this project (the smaller polynomials produce no useful sound). As you can see, it can produce an almost half-wave using the parabola. Parabolas in the form we have for f(x) can curve up or down from the origin with the only exception being straight lines when the A coefficient is 0. By changing the C coefficient, we can change where we start on the line. You can see that there are a few curves that start at the top of the graph and head down and a few that start at the bottom of the graph and head up. I could go on describing these curves, but you get the picture. Unfortunate 71 was created using a polynomial with 71 coefficients, which is rather difficult to print, but why not?

f_71(x) = A_0 + A_1*x + A_2*x**2 + A_3*x**3 + A_4*x**4 + A_5*x**5 + A_6*x**6 + A_7*x**7 + A_8*x**8 + A_9*x**9 + A_10*x**10 + A_11*x**11 + A_12*x**12 + A_13*x**13 + A_14*x**14 + A_15*x**15 + A_16*x**16 + A_17*x**17 + A_18*x**18 + A_19*x**19 + A_20*x**20 + A_21*x**21 + A_22*x**22 + A_23*x**23 + A_24*x**24 + A_25*x**25 + A_26*x**26 + A_27*x**27 + A_28*x**28 + A_29*x**29 + A_30*x**30 + A_31*x**31 + A_32*x**32 + A_33*x**33 + A_34*x**34 + A_35*x**35 + A_36*x**36 + A_37*x**37 + A_38*x**38 + A_39*x**39 + A_40*x**40 + A_41*x**41 + A_42*x**42 + A_43*x**43 + A_44*x**44 + A_45*x**45 + A_46*x**46 + A_47*x**47 + A_48*x**48 + A_49*x**49 + A_50*x**50 + A_51*x**51 + A_52*x**52 + A_53*x**53 + A_54*x**54 + A_55*x**55 + A_56*x**56 + A_57*x**57 + A_58*x**58 + A_59*x**59 + A_60*x**60 + A_61*x**61 + A_62*x**62 + A_63*x**63 + A_64*x**64 + A_65*x**65 + A_66*x**66 + A_67*x**67 + A_68*x**68 + A_69*x**69 + A_70*x**70

Most mathematicians would describe this differently of course. Here's a preferable notation for this function.

f_71(x) = A_0 + A_1*x + A_2*x**2 + ... + A_70*x**70

Or we could use summation notation which I'm not willing to get into in this blog in the interest of saving time. Shall I draw you 50 polynomials from Unfortunate 71? It's a little bit ugly, I must admit. The reason I'm not releasing the source code is because I plan to improve upon this. Anyway, here it is.

Unfortunate List by Javantea is licensed under a Creative Commons Attribution 3.0 Unported License.

Permissions beyond the scope of this license may be available at http://sono.us/cc.

**Unfortunate 3**

- Ogg Vorbis (4.7 MB)
- FLAC (5.2 MB)

**Unfortunate 8**

- Ogg Vorbis (5.3 MB)
- FLAC (8.2 MB)

**Unfortunate 11**

- Ogg Vorbis (5.4 MB)
- FLAC (8.9 MB)

**Unfortunate 71**

- Ogg Vorbis (5.3 MB)
- FLAC (12 MB)

Javantea out.

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