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## #1 2006-08-01 23:36:33

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

### 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??

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## #2 2006-08-02 02:13:53

Patrick
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Registered: 2006-02-24
Posts: 1,005

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

neat indeed

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## #3 2006-08-02 07:30:58

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

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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## #4 2006-08-02 08:03:47

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

### 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..."

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## #5 2006-08-02 08:35:42

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

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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## #6 2006-08-02 08:38:25

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

Ricky wrote:

You mean 10x1000, no?

Yes

IPBLE:  Increasing Performance By Lowering Expectations.

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## #7 2006-08-02 08:46:42

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

Connecting the points:

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

IPBLE:  Increasing Performance By Lowering Expectations.

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## #8 2006-08-02 09:52:22

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

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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## #9 2006-08-02 09:54:15

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

IPBLE:  Increasing Performance By Lowering Expectations.

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## #10 2006-08-02 09:55:37

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

### 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 (2006-08-02 09:57:54)

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## #11 2006-08-02 09:57:19

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

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

Pictures 1-5:

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

IPBLE:  Increasing Performance By Lowering Expectations.

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## #12 2006-08-02 10:01:12

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

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

Pictures 6-10:

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

IPBLE:  Increasing Performance By Lowering Expectations.

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