One Amazing Graph!

[Bizza]

Hi gang!

 

This is my first real post and I read the rules and T&C's and hope I'm not breaking them and hope this is the right section for this?

 

Anyway... I have something weird to share with you all. It took me a long time to really make this public, but here it is and I hope you all try it for yourselve's and give me any feedback?

 

...

I thought I'd share this very interesting graph I discovered in our times-table around 5 years ago (November 2004). I have aptly named it "OneEye" or "1i".

 

There's an interesting story behind its discovery and, it's a result of graphing the times-table after using what is known as the "Rule Of 9", where each number is reduced to a single digit-root sum (one single number). For example; if we took 8x4 = 32, the single digit would be 5 (3+2). Again if we took say; 3x4 = 12, the single digit root would be 3. Easy enough hey? Once you do this with every number in the times-table, you get a repeating block of numbers that repeat over and over in a 9x9 block. This block of numbers is also known as the "Vedic Square" and looks like this:

123456789

246813579

369369369

483726159

516273849

639639639

753186429

876543219

999999999

 

When you surround this block with all 9's (as it naturally should be if you look at the repeating blocks in the times-table), you should get this:

9999999999

9123456789

9246813579

9369369369

9483726159

9516273849

9639639639

9753186429

9876543219

9999999999

 

If you graph this using MS-Excel (using the surface-wireframe-contour graphing tool), you get one amazing graph.

 

 

When I discovered this for the first time, my jaw dropped and I stared at it for a good hour or two wondering what the heck it was? This then led me to an exponential learning curve like I've never experienced and, very quickly, it opened the door for me to learn many other things about Science, Art, Epistemology and much more. None moreso than my re-discovery of the irrational number/ratio Phi (1.618). I mean, I've studied Science (Physics, Mathematics) and have seen graphs and fractals of all kinds, but never something like this and in such a simple way.

 

I have dedicated a site specifically for this called EyePhi.com. There's more to it and if you look into the pupil, you may see some other perplexing images of animals, food and religious/spiritual symbols as well. This is up for interpretation and only relative to the observer, of course. But for me, it is more than just a graph!

 

Cheers!

-Bizza.

Edited September 21, 2009 by Bizza

[randomc]

looks like turtle shell road kill to me.

[dr.syntax]

Why didn`t you provide a link ? I distrust postings that leave out such an obviously helpful method of looking at what they have to say. ...ds

[Bizza]

Why didn`t you provide a link ? I distrust postings that leave out such an obviously helpful method of looking at what they have to say. ...ds

 

I thought I did? I just didn't want to link it to my site due to the rules here. But here it is again... EyePhi.com. I'd really apreciate your views though matey. What do you think? Cheers!

---

Merged post follows:

Consecutive posts merged

looks like turtle shell road kill to me.

 

LOL awesome! What else can you see?

Edited September 22, 2009 by Bizza
Consecutive posts merged.

[CaptainPanic]

Ok, so I also "created" this thing. It's funny, but I fail to see why it's so amazing. Yes, there are certain patterns. But I'm not sure that you're looking at the right thing when you're wondering what kind of animal or object you're seeing. There are patterns in the tables of 1-9... nothing new. Perhaps it's because they're tables (you add the same number every time again)?

 

For those mystified by the concept of the "surface-wireframe-contour graphing tool", all it does is to plot on a square the contours of the map that you have... same as in geography... except that this is a very rudimentary version which doesn't make smooth (rounded) lines, but puts pointy angles in it.

 

All the values in the matrix become a "height", and Excel creates a bunch of lines that connect where the same height occurs. It creates a large number of data-points that are NOT in the matrix itself. With the right function, I am sure you could even make the "Eye" more smooth, and looking more natural.

 

I am not sure what the point is of this thread. Are we investigating anything?

 

If you want to make your "eye" even prettier, you should use a better plotting tool (Gnuplot for example? I'm not sure which is the best). Alternatively, you can plot a 3D version of the "eye", and change the perspective in Excel. You can also add color.

But most importantly: if you plot something, don't delete the legend or remove colors (which you did). Why remove information??

 

[edit] If you're so fascinated by numbers, why not start plotting the prime numbers, and see if you can find a pattern there? I'm sure that if you develop a tool to predict the next prime number without some serious number crunching on super computers, you'll be famous. In case you're wondering: the prime numbers are all those numbers that you do not find in your matrix (minus a few which are 11x, 12x, 13x etc a certain number).

Edited September 22, 2009 by CaptainPanic

[Bizza]

Ok, so I also "created" this thing. It's funny, but I fail to see why it's so amazing. Yes, there are certain patterns. But I'm not sure that you're looking at the right thing when you're wondering what kind of animal or object you're seeing. There are patterns in the tables of 1-9... nothing new. Perhaps it's because they're tables (you add the same number every time again)?

 

For those mystified by the concept of the "surface-wireframe-contour graphing tool", all it does is to plot on a square the contours of the map that you have... same as in geography... except that this is a very rudimentary version which doesn't make smooth (rounded) lines, but puts pointy angles in it.

 

All the values in the matrix become a "height", and Excel creates a bunch of lines that connect where the same height occurs. It creates a large number of data-points that are NOT in the matrix itself. With the right function, I am sure you could even make the "Eye" more smooth, and looking more natural.

 

I am not sure what the point is of this thread. Are we investigating anything?

 

If you want to make your "eye" even prettier, you should use a better plotting tool (Gnuplot for example? I'm not sure which is the best). Alternatively, you can plot a 3D version of the "eye", and change the perspective in Excel. You can also add color.

But most importantly: if you plot something, don't delete the legend or remove colors (which you did). Why remove information??

Thanks CaptainPanic, I appreciate that. There's no real significance to some maybe, but, it is quite perplexing that a depiction of an "eye" can be created using this technique and in such a simple way, don't you think? It's not like I made up the numbers did I? It was straight from our times-table (after reducing each number to its root digit).

 

If you're a religious or spiritual person, there's some other things about it that strikes a cord, particularly for Muslim's. For example, Gematria, Vedic's, Dejjal (One eye'd Anti-Christ) comes to mind, but that's if your theistic of course. It's just that it's quite weird that no other image can be produced using this technique. If so, I'd love to see it?

 

By the way, how do I make the eye smoother and in 3D (except for using the 3D surface graphing tool, which shows nothing really!)? Also, I removed the legends to make the graph look a bit better. The legends don't really help anyway (to most people that don't know anything about graphing).

 

I've got different versions of this in different colours as well, but I thought I'd leave it blank and to leave it to the viewer's imagination to colour it in.

 

Thank you very much matey and if you have any other ideas or input, that would be appreciated. There's also a math dep't (on Vedic Maths) writing an article about this in their newsletter this month and the story that followed my discovery is also going to be featured in a book in the US soon as well.

 

Cheers mate and thanks again.

 

[edit] ummmm... I think that the numbers 2, 3, 5 & 7, are Primes. And I will have a look at them another time maybe. I'm just so tired of "number-crunching" at the moment. I'm more of a theoretical scientist, rather than a 'number lover'... hehe. Cheers again!

Edited September 22, 2009 by Bizza

[JillSwift]

There isn't much amazing about pareidolia.

[the tree]

There are certainly more interesting plots out there.

 

There's various fractals, population models, the Gamma Function even nearly random plots have their own charm.

[Bizza]

There isn't much amazing about pareidolia.

Sure, I know if you look at the clouds and look at the sand at your feet, I'm sure one can make out just about anything really. But, what makes this interesting (for me anyway) is what followed after it. I had one really amazing year following it. It was a sort of "trigger" or "catalyst" for my increase in inquizitiveness in many areas of study. Each to their own though hey?

---

Merged post follows:

Consecutive posts merged

There are certainly more interesting plots out there.

 

There's various fractals, population models, the Gamma Function even nearly random plots have their own charm.

Yes, all good and great, although the only interesting one there would be fractal's, but they're produced using complex polynomial equations, whereas OneEye is not. That's why it intrigues me more than any other at the moment. As I mentioned before, I have seen many many types of graphs and fractals but never anything like this and in such a simple way.

 

Thanks Tree, I appreciate your input though.

[CaptainPanic]

For good 3D, you need a different tool. I am not interested enough to try it, but I know that Gnuplot should be able to do quite amazing stuff. Not sure if it will work easily, because I think (not sure) that you need to provide the input i the form of a script (sort of like a textfile - and for that you might need to know the Octave/Matlab language)?

 

Perhaps others can tell us how to make nice 3D contour plots.

 

The smoothness has to be in the plotting tool already, or alternatively, you can just generate more data. Since we're just dealing with contours, you can take your matrix of numbers (link to OP's personal wikipedia website) and put it in Excel. Then create an empty line between all the rows, and between all the columns. Then fill up the newly created empty spaces with the average values:

Directly between two numbers, it's just (X+Y)/2. For the ones diagonally between 4 numbers, you take (A+B+C+D)/4. Or, alternatively, the average of the newly created averages.

Now you created a 19x19 matrix, with a lot more numbers... The whole operation shouldn't take more than 5 minutes.

 

And that will create another eye, which looks like in the attachment.

[Bizza]

For good 3D, you need a different tool. I am not interested enough to try it, but I know that Gnuplot should be able to do quite amazing stuff. Not sure if it will work easily, because I think (not sure) that you need to provide the input i the form of a script (sort of like a textfile - and for that you might need to know the Octave/Matlab language)?

 

Perhaps others can tell us how to make nice 3D contour plots.

 

The smoothness has to be in the plotting tool already, or alternatively, you can just generate more data. Since we're just dealing with contours, you can take your matrix of numbers (link to OP's personal wikipedia website) and put it in Excel. Then create an empty line between all the rows, and between all the columns. Then fill up the newly created empty spaces with the average values:

Directly between two numbers, it's just (X+Y)/2. For the ones diagonally between 4 numbers, you take (A+B+C+D)/4. Or, alternatively, the average of the newly created averages.

Now you created a 19x19 matrix, with a lot more numbers... The whole operation shouldn't take more than 5 minutes.

 

And that will create another eye, which looks like in the attachment.

Awesome! That was very helpfull mate. Thanks for that.

 

LOL! By the way, the link you gave was my own graph above. I'm surprised you didn't see that? hehe. Anyway, I'll try and look at other ways of smoothing OneEye a bit more another time, but your advice was very helpful CaptainPanic. Highly appreciated buddy. I think I may mention this on my site (crediting you with it too if you don't mind?)

[Bizza]

Just for fun, here's another version with OneEye's grid erased and sraightened 45 degrees. Maaaaan I had alot of fun with this when I first discovered it. You guys just reinvigourated it. Thanks a million gang!

[JohnB]

CaptainPanic, what's the bet that your diagram is going to turn up somewhere in a year or so as the "schematic" of a flying saucer?

[the tree]

Yes, all good and great, although the only interesting one there would be [fractals],

Subjectively speaking, maybe. But take a serious look at the gamma function over the complex plane and tell me there isn't a beauty about it.

but they're produced using complex polynomial equations, whereas OneEye is not.

Not all fractals take complex numbers, nor are they frequently very complicated. Take the logistic map for instance - chaotic but from a very simple system and I would say the majority of fractals aren't based around polynomials - think Sierpiński gaskets, space filling curves, Lorenz attractors...

[CaptainPanic]

LOL! By the way, the link you gave was my own graph above.

 

Umm... well... I did call it your personal wikipedia page.

BTW, it's being edited right now (which is why linking to wikipedia can be a bad thing!!), and the picture disappeared, and mathematical symbols and explanations start to appear... including a reference. (Or was that there before?)

Anyway - too bad for you about the picture, but IMHO, the site is becoming better.

I think I may mention this on my site (crediting you with it too if you don't mind?)

Just link to this forum and thread, and you should be fine.

 

CaptainPanic, what's the bet that your diagram is going to turn up somewhere in a year or so as the "schematic" of a flying

saucer?

 

I really hope that they convert it to a .jpg (instead of my nasty .bmp) before then, or all the extraterrestrial servers will grind to a halt.

Edited September 22, 2009 by CaptainPanic

[Bizza]

Subjectively speaking, maybe. But take a serious look at the gamma function over the complex plane and tell me there isn't a beauty about it.

Not all fractals take complex numbers, nor are they frequently very complicated. Take the logistic map for instance - chaotic but from a very simple system and I would say the majority of fractals aren't based around polynomials - think Sierpiński gaskets, space filling curves, Lorenz attractors...

Yes true, and it is very beautiful indeed. I particularly like the Julia & Madlebrot sets. They are so cool! I wonder, do you think that our universe is a fractal of sorts in a more complex way? Given that there's an opposite to everything, one could almost say that there's a hidden universe within (or outside)? Just a thought. Thanks matey.

---

Merged post follows:

Consecutive posts merged

Umm... well... I did call it your personal wikipedia page.

BTW, it's being edited right now (which is why linking to wikipedia can be a bad thing!!), and the picture disappeared, and mathematical symbols and explanations start to appear... including a reference. (Or was that there before?)

Damn! Someone edited out my picture whilst we were posting? That was there before, but was added to the existing info. Anyway, at least I have the proof from a long time ago. Do you think I could get it added again? Gee Wicki can be so crap sometimes LOL!

Anyway - too bad for you about the picture, but IMHO, the site is becoming better.

You mean my site or Wicki's?

Just link to this forum and thread, and you should be fine.

Sure, done! Thanks matey!

Edited September 22, 2009 by Bizza
Consecutive posts merged.

[CaptainPanic]

You mean my site or Wicki's?

I meant wikipedia.

Your picture is just one type of plot of the data, and doesn't seem to add information... although it looks nice. There are many other types of plots that can show the same information.

 

The real issue is the Vedic square, not the eye.

[Bizza]

I meant wikipedia.

Your picture is just one type of plot of the data, and doesn't seem to add information... although it looks nice. There are many other types of plots that can show the same information.

 

The real issue is the Vedic square, not the eye.

Fair enough. I know the Vedic Square is the topic on Wicki, but "geometric patterns" was also a mention there and that's why my graph was included as one of them. Surprised that they would mention that, yet exclude 'such patterns'? Not that I'm worried about it or anything.

Edited September 22, 2009 by Bizza

[the tree]

There's quite a few nice patterns that don't take adding any information.

 

Taking either 0-9x0-9 or 1-8x1-8:

 

Reflections about the vertical or horizontal centre lines interchanges pairs of numbers, specifically the ones that add up to nine. e.g. 2 and 7 switch places with a reflection, whereas the 9s are symmetric over those reflections.

 

The shape formed by each member of one of those pairs of numbers is unique to that pair so the square forms 5 distinct shapes each with rotational symmetry of degree 4 (or 10 with degree 2).

 

Quite a bit of information there already - little need to add more.

Edited September 22, 2009 by the tree

[dr.syntax]

I saw kites. Maybe you should provide the option for " OTHER " and a space for them to type in what they see instead of someone else`s choices. I am very reluctant to sign in to any site and didn`t. I`m sure you have your reasons but people like myself do not go around readily signing onto sites. I`m giving you some honest feed back. I expect you would get very many more people interested in exploring your website if you did away with that sign in requirement. Regards, ...Dr.Syntax

[Bizza]

There's quite a few nice patterns that don't take adding any information.

 

Taking either 0-9x0-9 or 1-8x1-8:

 

Reflections about the vertical or horizontal centre lines interchanges pairs of numbers, specifically the ones that add up to nine. e.g. 2 and 7 switch places with a reflection, whereas the 9s are symmetric over those reflections.

 

The shape formed by each member of one of those pairs of numbers is unique to that pair so the square forms 5 distinct shapes each with rotational symmetry of degree 4 (or 10 with degree 2).

 

Quite a bit of information there already - little need to add more.

Thanks Tree;). I'll try them all soon and see what comes up. Much appreciated.

---

Merged post follows:

Consecutive posts merged

I saw kites. Maybe you should provide the option for " OTHER " and a space for them to type in what they see instead of someone else`s choices. I am very reluctant to sign in to any site and didn`t. I`m sure you have your reasons but people like myself do not go around readily signing onto sites. I`m giving you some honest feed back. I expect you would get very many more people interested in exploring your website if you did away with that sign in requirement. Regards, ...Dr.Syntax

Thanks for your suggestion Dr.Syntax. I definately will add another page just like you said. By the way, you shouldn't have to sign in to make a comment. Or did it ask this first? I've allowed anyone to make comments without having to. But please do let me know if you have any troubles.

 

You are all wonderful people and I appreciate all your inputs. Thanks gang!

[the tree]

If you want to discuss the Vedic square properly then you could ask a mod to move this thread to the mathematics board, or start one yourself there. There's probably a whole load of algebraic and geometric properties that it's beyond my ability to notice just by inspection.

[Bizza]

If you want to discuss the Vedic square properly then you could ask a mod to move this thread to the mathematics board, or start one yourself there. There's probably a whole load of algebraic and geometric properties that it's beyond my ability to notice just by inspection.

I may just do that Tree. It sure is an interesting little topic as simple number theory. I'm just a bit busy these last couple of days, but I'll get on it. I should start a new thread there. Thanks again for all your input and suggestions champ.

 

Cheers!

[bascule]

Behold, the Julia set:

 

[Bizza]

Sheeeez perrrrty!!!