DNA Fractal DNA Fractal

Introduction

This piece depicts the first chromosome of my genome sequence as a pair of mirrored Sierpiński triangles. It is the third and final part of the MAD triptych (Music–Astronomy–DNA).

Data & Method

Raw genotype data from a 23andMe test I took in early 2023 was used to generate this piece. Each row in the raw data table corresponds to an SNP (single-nucleotide polymorphism).^aaThey account for most genetic variation between humans. For each SNP, the data provides its identifier (an rsID or an internal ID), its position on the reference human genome, and the genotype call oriented with respect to the plus (forward) strand of the human reference sequence. Reference human assembly build 37 was used for my genome.^bbA reference genome is a composite — no single person’s DNA, but a mosaic assembled from multiple anonymous donors. Individual variants are defined by their deviation from this agreed-upon coordinate system. The raw data was cleaned programmatically, and a colour was assigned to each of the 20 distinct genotype calls.

These calls are marked in the legend with coloured labels (either a single letter or two letters) and triangles. I also indicate the geometric framework of the composition using the indices, which reveal how the sequential rows get arranged into the pyramidal structure. Perhaps my childhood fondness for Toblerone and for building houses of cards helped inspire this result. The fractal Sierpiński triangle was generated using Python code I wrote. I generated a separate fractal triangle for each chromosome. Each genotype call at SNP loci is thus encoded by one of the coloured triangular units. I also played around with using different fractal shapes (such as the Koch snowflake) for different chromosomes.

Fractal Structure

I include a helpful depiction of the way the recursion manifests in the visual using these magnified sections. The white padding (triangles labelled NA) in the legend was necessary since the number of SNPs per chromosome does not line up with the number that makes a complete fractal of the corresponding level.

The number of triangles at each level n follows the formula: T_n = 3ⁿ

A subsidiary legend in the bottom left marks which chromosome the data is from.

Symbolism & Meaning

This visual is an attempt to paint with thought, to connect the beauty of emergent geometry with fundamental genetics. Different conformation forms of DNA are included in the margins, as is the X-ray crystallography image from Rosalind Franklin which was the key to understanding its double helical structure. The black negative spaces in the fractal are meant to represent the long stretches of non-coding DNA (98% in the human genome) whose function we do not yet fully understand.1 The recursive nature of a fractal mirrors the multiple iterations of folding of the information-dense molecule that enable its packing into cell nuclei. The calligram at the centre of each triangle is meant to bring to mind a bundle of densely coiled genetic material. I could go on endlessly about this piece, but I’ll cut the discussion at the first level (before it gets too recursive).

I placed a quote by Bouchard from a seminal study on human twins in the top-left margin. I wish more of modern scientific research maintained the tradition of poetic, moving prose that our predecessors established. At some point in the 20th century, beauty and science were brutally separated — one of the reasons I make these visuals is in the hope we can someday reunite them.

I am never entirely sure which corner of the subconscious some of these ideas come from. Those who met me during the neuroscience-focused years probably aren’t aware, but for a significant portion of my childhood I was very set on eventually becoming a genetic engineer. I had fallen in love with DNA when I read Michael Crichton’s Jurassic Park as a child.

After a semester-long stint doing wet-lab research as a freshman in college, I soon realised I really disliked babysitting cells. I did not enjoy being entirely unable to see what I worked with unless glued to a microscope. I also worked at a bioinformatics lab my sophomore year, which provided training for running analyses on high-performance computing clusters. I eventually ended up using that training for analysing structural brain networks rather than the mouse embryogenics project I had been assigned. I hope those mice found someone else to lend their sacrifice purpose.

I suspect this little piece, a fancy QR code for the substance of the soul, is in some intangible way worth more than any scientific research I would have produced had I gone on to become a geneticist. On a lighter note, it’s so supremely me to make something of this sort using my own DNA. It’s no coincidence that neuroscientist and narcissist are siblings by syllable.