This seems easy to achieve with raster graphics. Let's start with the following image:
Regarding the "not uniform in width" part, lines are wider where they are closer to other dark things. To achieve this:
- Gaussian blur
- Boost contrast to the max
Regarding the "texture" part, the dark areas are darker near their edges. To achieve this:
Sorry, my sharpen filter has too small a radius. You can play around with settings of all said filters.
Then you can convert it to vector graphics.
When working directly with vector graphics instead, the first step would be to "smoothen" the contours, see for example https://gis.stackexchange.com/questions/24827/smoothing-polygons-in-contour-map
- The aforementioned filters can be part of physical image acquisition or default scanner software
- From a scientific point of view, the aforementioned filters can be analyzed from the point of view of differential equations, and that can yield information about how the level sets evolve, i.e. how to smoothen the contours to achieve the same (up to numerical imprecisions) result.