in

NFTs family based on math theorem

Integer factorization (e.g.28=2x2x7) is apparently simple, however it is at the base of some not solved problems in mathematics: we do not know how to find the factors of a number through an efficient algorithm.

This fact is intriguing me, and I spent time to link integer factorization to images. I finally succeeded to iteratively fragment polygons in exactly n tiles according to factors of n,  and coloring them in HSI space : Hue and Intensity are functions of smaller factors for global view and of largest factor for details.

You can see number 10005=3x5x23x29 in the following image, it is made exactly of 10005 tiles. You can also see how colors change on global areas (e.g. 3 and 5 factors) and intensity on details (e.g. 29 factor).

As factorization results are not predictable, the image sequence (image of each n) is not predictable. In addition, as factorization is unique (unique-prime-factorization theorem), each created image is unique! …and to honor mathematical one-to-one correspondence I will create no more than one NFT for each number n !

I am wondering which types of numbers would be more marketable (e.g. birthdates, IDs, geo-coordinates) and where they should be published. 

I must take into account that processing time increases exponentially with the number of digits (my home PCs digests in few seconds “n” around some tens of thousands) and “higher n” implies “higher number of tiles”, which implies “higher image resolution needed for details”. Any suggestions are more than welcome. 

Here below you can see 9 different images/numbers around 10000.

Interestingly, I spent time to achieve symmetry in geometry and color space during the fragmentation/ iteration process (this was one of the most difficult challenges for me), however, once I got it, I had to inject a small % of asymmetry for better artistic results: it seems that our brain (at least mine) likes harmony but not full perfection! 

As additional example, the image below is n= 10008=2x2x2x3x3x139, I put this one on NFTAggregator market place. I like it for the effects of many small factors vs one big factor.

Now I am working on some variations of the algorithm, ciao 

< Made in @ProcessingOrg /python | TW, IG, OpenSea: by @Leonardo5mARTh >

Written by Leonardo5mART

Leave a Reply

Elon Musk Imperator Of Mars

Three Lions EURO2020 NFTs #s 1, 2, 3 & 4