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**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

i was programming a program that can generate all numbers, then delete all primes/squares/palindromes etc, or keep them, and also painting a picture with dots at the numbers positions (and no dot where a nmber has been deleted).

when playing around with it i noticed a very cool thing

i rendered all numbers from 0 to 10000. then it looks like this:

http://www.geocities.com/tibiihost/all_numbers.bmp

every green dot is a number, and it is 10 numbers (10 pixels) wide. so for example the first line are numbers 0 to 9, 2nd are 10 to 19, the last line is 990 to 999 and the last dot is 1000 etc.

then i kept all perfect squares, removed all other numbers:

http://www.geocities.com/tibiihost/all_Squares.bmp

look at the pattern! it forms some kind of wave. btu that isnt everything

i removed all odd numbers, kept all even squares, and the dots remaining formed another wave shape, but reversed

http://www.geocities.com/tibiihost/all_Even_Squares.bmp

cool eh??

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

neat indeed

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

Interesting. Here's a picture 10x10000:

*Last edited by krassi_holmz (2006-08-02 07:34:54)*

IPBLE: Increasing Performance By Lowering Expectations.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

You mean 10x1000, no?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

Here's better:(It's flipped)

*Last edited by krassi_holmz (2006-08-02 08:42:13)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

Ricky wrote:

You mean 10x1000, no?

Yes

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

Connecting the points:

*Last edited by krassi_holmz (2006-08-02 08:47:06)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

I have played for a while with mathematica, and I founded interesting patterns.

The code:

```
ToCoords[x_][c_] := {Floor[c/x], c - x Floor[c/x]};
SqueezedDotPlot[x_, list_, ops___] := Show[Graphics[Point /@ (ToCoords[x] /@ list)], ops];
SqueezedLinePlot[x_, list_, ops___] := Show[Graphics[Line[ToCoords[x] /@ list]], ops];
```

Here I will actually use only the first plotting function.

Picture 1: this is the actual square function.

`SqueezedDotPlot[10, Range[100]^2]`

Picture 2: If you use irrational numbers, there can be interestiong results.

`SqueezedDotPlot[4, Range[1000]^Sqrt[2]]`

Picture 3: But for most of the numbers, you will get the ordinary noise.

`SqueezedDotPlot[Sqrt[10], Range[10000]^3]`

Picture 4: Some non-trivial structure

`SqueezedDotPlot[Sqrt[2], Range[10000]^2]`

Picture 5: The previous zoomed

`SqueezedDotPlot[Sqrt[2], Range[1000]^2]`

Picture 6: Noise again, but different from the ordinary.

`SqueezedDotPlot[3, Range[10000]^1.5]`

Picture 7: And what if the exponent is smaller than 1?

`SqueezedDotPlot[2, Range[10000]^0.9]`

Picture 8: interesting...

`SqueezedDotPlot[1, Range[10000]^0.99]`

Picture 9: What a wave!

`SqueezedDotPlot[2, Range[10000]^0.999]`

Picture 10: this is beautiful!!!

`SqueezedDotPlot[0.1, Range[10000]^0.5]`

*Last edited by krassi_holmz (2006-08-02 09:55:32)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

I'll upload the pictures soon...

IPBLE: Increasing Performance By Lowering Expectations.

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**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

http://www.geocities.com/tibiihost/Squarelines.bmp

seems like the odd numbers are like the line including all numbers but much more angular with less dots

edit :

I'll upload the pictures soon...

nice, cool, im waiting

*Last edited by Kurre (2006-08-02 09:57:54)*

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

Pictures 1-5:

*Last edited by krassi_holmz (2006-08-02 09:58:38)*

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,906

Pictures 6-10:

*Last edited by krassi_holmz (2006-08-02 10:05:37)*

IPBLE: Increasing Performance By Lowering Expectations.

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