Primes as pictures

[pepi37]

Lets say we have mega prime
So it can put in matrix of 1000*1000 pixels and then any of number in prime can be associated by another color.

I look for solution where I can

a: change size of matrix
b change "color" of numbers as I wish

Did you seen something like that on Net?

[Batalov]

https://www.rstudio.com/wp-content/u...cheatsheet.pdf

https://wiki.nbic.nl/index.php/R_ggplot2_tutorial

or similar tools in python

[pepi37]

Thanks!
I will now look at those links!

[storm5510]

Originally Posted by pepi37

Lets say we have mega prime
So it can put in matrix of 1000*1000 pixels and then any of number in prime can be associated by another color...

I did something similar to this a few years ago. The most recent prime, which I believe to be M74207281, has 22,338,618 digits. If one wanted a truly square image, then said image would need to be 4327 x 4327 pixels. I arrived at this by taking the square root of the number of digits, and rounding up. This probably coudn't be done on a screen, but I believe ti could be done in RAM then saved to a bitmap file. Using colors could be misleading. I would use grayscale. A value of 0 (zero) would be white, and 9 would be black. The values between could be represented by increasing the grayscale value by 25.

[CRGreathouse]

I used something like this as my profile picture on mymathforum for many years.

[chalsall]

Originally Posted by storm5510

A value of 0 (zero) would be white, and 9 would be black. The values between could be represented by increasing the grayscale value by 25.

Based on your rules, wouldn't you immediately switch white to black?

[storm5510]

Originally Posted by chalsall

Based on your rules, wouldn't you immediately switch white to black?

No, not for decimal numbers Below is a table of values for each decimal number, using the RGB color model.

0 = 250,250,250
1 = 225,225,225
2 = 200,200,200
3 = 175,175,175
4 = 150,150,150
5 = 125,125,125
6 = 100,100,100
7 = 50,50,50
8 = 25,25,25
9 = 0,0,0

If a person has the prime number in a text document, for example, you would read it, one digit at a time, and assign a color value, then place in the bitmap, starting at coordinate 0,0, then proceed right until coordinate 4326,0 was reached. Drop down to coordinate 0,1 and continue from there, repeating the process until the images was complete.

It would depend on what type of monitor a person has in regards to being able to see the entire image, without some type of resampling.

[Jayder]

I've been working on this as a side project for over a year. I'm having problems with R where lines that should overlap do not, and I can't figure out a way to correct that. The following images are intentionally in low resolution, because it does not meet my standards:

M49, base 10

M30, base 6

This is a common idea, but I got it specifically from Nadieh Bremer. I will point you to her wonderful blog for the explanation of these: https://www.visualcinnamon.com/portfolio/the-art-in-pi (Her code has a few quirks and has trouble with large numbers, so I rewrote the bulk of it.)


I also converted M49 to base 2^24-1 in order to have (almost) every colour in the 24-bit colour space represent a digit. Here is that image (I cannot upload it to a hosting site because they compress large files): Google drive link

[storm5510]

Originally Posted by Jayder

...I also converted M49 to base 2^24-1 in order to have (almost) every colour in the 24-bit colour space represent a digit. Here is that image (I cannot upload it to a hosting site because they compress large files): Google drive link

When whoever converted it to a PNG, a lot of data was lost in that instant. It got very fuzzy when I zoomed in. Still, this is a good example of what an image representation can look lilke.

[chalsall]

Originally Posted by storm5510

Still, this is a good example of what an image representation can look like.

Are you guys reproducing work which has already been done? Please see as an example.

Amusingly, I remembered this previous work, and first searched using Google Images using the term "Prime Curve".

This is the result I got back. And, of course, my girlfriend then immediately entered the room asking what I would like for dinner.

Thankfully she has a good sense of humour, but I'm going to cook tonight....

[Jayder]

Originally Posted by storm5510

When whoever converted it to a PNG, a lot of data was lost in that instant. It got very fuzzy when I zoomed in. Still, this is a good example of what an image representation can look lilke.

You were supposed to download it, not view the preview. I guess I wasn't clear.

Originally Posted by chalsall

Are you guys reproducing work which has already been done? Please see as an example

Hopefully everybody here is familiar with Ulam's spiral already. What is the reason for your question, anyhow? I've already admitted that this is not an original idea.