Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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?? big_smile

Offline

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

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

Re: Perfect Squares forming some kind of wave

neat indeed smile


Support MathsIsFun.com by clicking on the banners.
What music do I listen to? Clicky click

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

Interesting. Here's a picture 10x10000:

View Image: sq10x10000.GIF

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

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

Ricky
Moderator
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..."

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

Here's better:(It's flipped)

View Image: sq1000x10.GIF

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

Ricky wrote:

You mean 10x1000, no?

Yes smile smile smile


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

Connecting the points:

View Image: sq1000x10lines.GIF

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

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.

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

I'll upload the pictures soon...


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#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 :

I'll upload the pictures soon...

nice, cool, im waiting tongue

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

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

Pictures 1-5:

View Image: sqz1.GIF View Image: sqz2.GIF View Image: sqz3.GIF View Image: sqz4.GIF View Image: sqz5.GIF

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

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

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Perfect Squares forming some kind of wave

Pictures 6-10:

View Image: sqz6.GIF View Image: sqz7.GIF View Image: sqz8.GIF View Image: sqz9.GIF View Image: sqzten.GIF

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


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

Board footer

Powered by FluxBB