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## #1 2006-08-02 21:36:33

Kurre
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### Perfect Squares forming some kind of wave

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??

## #2 2006-08-03 00:13:53

Patrick
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### Re: Perfect Squares forming some kind of wave

neat indeed

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## #3 2006-08-03 05:30:58

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

Interesting. Here's a picture 10x10000:

Last edited by krassi_holmz (2006-08-03 05:34:54)

IPBLE:  Increasing Performance By Lowering Expectations.

## #4 2006-08-03 06:03:47

Ricky
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### Re: Perfect Squares forming some kind of wave

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..."

## #5 2006-08-03 06:35:42

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

Here's better:(It's flipped)

Last edited by krassi_holmz (2006-08-03 06:42:13)

IPBLE:  Increasing Performance By Lowering Expectations.

## #6 2006-08-03 06:38:25

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

#### Ricky wrote:

You mean 10x1000, no?

Yes

IPBLE:  Increasing Performance By Lowering Expectations.

## #7 2006-08-03 06:46:42

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

Connecting the points:

Last edited by krassi_holmz (2006-08-03 06:47:06)

IPBLE:  Increasing Performance By Lowering Expectations.

## #8 2006-08-03 07:52:22

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

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

#### 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.

#### Code:

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

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

#### Code:

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

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

#### Code:

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

Picture 4: Some non-trivial structure

#### Code:

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

Picture 5: The previous zoomed

#### Code:

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

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

#### Code:

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

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

#### Code:

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

Picture 8: interesting...

#### Code:

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

Picture 9: What a wave!

#### Code:

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

Picture 10: this is beautiful!!!

#### Code:

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

Last edited by krassi_holmz (2006-08-03 07:55:32)

IPBLE:  Increasing Performance By Lowering Expectations.

## #9 2006-08-03 07:54:15

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

IPBLE:  Increasing Performance By Lowering Expectations.

## #10 2006-08-03 07:55:37

Kurre
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### Re: Perfect Squares forming some kind of wave

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 :

nice, cool, im waiting

Last edited by Kurre (2006-08-03 07:57:54)

## #11 2006-08-03 07:57:19

krassi_holmz
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### Re: Perfect Squares forming some kind of wave

Pictures 1-5:

Last edited by krassi_holmz (2006-08-03 07:58:38)

IPBLE:  Increasing Performance By Lowering Expectations.

krassi_holmz
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Pictures 6-10: