Suppose one has a fairly long segment of nucleotide letters ATGC. A way to form an image, based on the Chaos Game Representation of Jeffrey, is as below. I use a pixellation level of 256x256 (2^8 x 2^8).
chars = {"A", "T", "G", "C"};
dim = 8;
makePositionsC = Compile[{{shifts, _Integer, 2}, {k, _Integer}},
Module[{posns},
posns = FoldList[Mod[2*#1 + #2, 2^k] &, Reverse@shifts];
Most[Reverse[Map[{2^k, 1} + {-1, 1}*Reverse[#] &, posns]]]
], RuntimeOptions -> "Speed", CompilationTarget -> "C"];
replace =
Dispatch[Thread[chars -> {{0, 0}, {0, 1}, {1, 1}, {1, 0}}]];
FCGR[chars_, alphabet_List, k_] := Module[
{shifts, posns, newposns},
shifts = chars /. replace;
newposns = Round[makePositionsC[shifts, k]];
Normal[SparseArray[Apply[Rule, Tally[newposns], {1}], {2^k, 2^k}]]
]
To give some idea of what gets produced, here are pictures from the six genomes discussed in one of the articles I referenced in my earlier reply. If the images are in an array images then further processing was done to get a reasonable gray scale:
scaledimages=Map[(#/N[Max[#]])^(1/6) &, images];
References
-
Jeffrey, H.: Chaos Game Representation of gene structure. Nucleic Acids Research 18(8), 2163–2170 (1990)
-
Lila Kari, Kathleen A. Hill, Abu S. Sayem, Rallis Karamichalis, Nathaniel Bryans, Katelyn Davis, Nikesh S. Dattani.
Mapping the Space of Genomic Signatures. [1406.4105] Mapping the Space of Genomic Signatures -
Rallis Karamichalis , Lila Kari , Stavros Konstantinidis and Steffen Kopecki,
An investigation into inter- and intragenomic variations of graphic genomic signatures
https://wolfr.am/fycQFg15
Wolfram Language code by the first listed coauthor can be found at the link below.
- Karamichalis R. Source code for computing FCGR matrices, distance matrices, MultiDimensional Scaling and separation planes.
GitHub - rallis/GenomicSignatures: Code for Genomic Signatures for "Additive Methods for Genomic Signatures" · GitHub.
Accessed 27 Jul 2016.
I use this in work that will be shown at SYNASC 2016 (Numerical Computing session 1).
http://synasc.ro/2016/list-of-papers
Full details for obtaining the genome nucleotide sequences are in the code appendix (not sure when this will appear though), or see Rallis Karamichalis’ web page.