A LinkedIn Cover That Isn’t Stock

My LinkedIn cover used to be a purple gradient with the company’s tagline on it. It works for the company page. My profile is my own surface, so I wanted a cover that read as mine: a quiet, monochrome plot in the same palette as this blog, with no words trying to sell anything.

The final result is one line of math and one curve:

The equation is geometric Brownian motion,

\[dX_t = \mu X_t\,dt + \sigma X_t\,dW_t\]

the process Black-Scholes assumes for the underlying. The curve is a single realized path: exponential drift, Brownian noise. Same idea as the volatility smile page I wrote earlier. The elegant model, and what actually happens when you let randomness in.

A few decisions along the way were deliberate.

A cover should be ambient

A LinkedIn banner is background. People come to the profile for the bio, the experience, the work. So the cover gets three elements and nothing else: the curve, a caption, and a URL. No axes, no ticks, no gridlines inside the plot. If the values don’t matter, the scaffolding is noise. I kept the graph-paper grid from this blog’s background, because it gives the curve a sense of place without making it a chart.

Grey, not black, not blue

I spent a while on color before landing on none. The data-viz literature converges on “grey plus one accent” for figures where a specific element matters. But a cover is the opposite situation: nothing in it should compete with the content below it. So the curve and caption are a mid grey, the URL is a little darker for legibility, and there is zero hue. Monochrome is the look this blog already has; the cover just commits to it harder.

Text on a cover dies

My first versions had the equation floating in the upper band, then as a caption at the bottom, then on the left. The placement that survived is symmetric: URL top-right, equation bottom-right, both right-aligned to the same column. An equation is content that describes the visual, so it sits on the visual like a caption. The URL is a signature, so it sits in the corner like one. Two text elements, two jobs, no overlap.

The crispness problem

The annoying part was output quality. Screenshot the HTML at 1x and a 2px curve is 2 physical pixels. It comes out soft and aliased, and LinkedIn’s own compression makes it worse. The fix is a pipeline I now use every time I turn HTML into an image:

1. Render in headless Chrome at 3x with --force-device-scale-factor=3, giving a 4752x1188 master where every line and glyph has real antialiasing data.
2. Downscale to the exact target with Pillow’s LANCZOS resampler. sips -z is bilinear and softens edges; LANCZOS is the right filter.
3. Save as PNG, or JPEG around q=90 for a much smaller upload.

The text needed to be a touch bigger than I first wanted (17px, not 15px). At 1584px wide, small glyphs are at the legibility floor, and shrinking them to fit the canvas just makes them blur.

The tool

All of it is one Python file now, so the next cover is one command:

kcover --seed 42 --out cover.png

It simulates a fresh path each run. Same equation, different realization, which is the point. The seed pins a specific draw if you want to keep one. It renders, downscales, and verifies the curve doesn’t collide with the equation or the URL.

Repo: github.com/kovashikawa/kcover

The cover is live on my profile. If you see it in the wild, the curve you’re looking at is one sample path of a stochastic differential equation. That’s the whole joke.