I’ve mentioned that subdividing an image is useful for putting patterns within the divisions. This method uses the outline of the subdivisions to provide the darkness. The way this is done is to repeatedly break a shape into two parts: ensuring that the ratio of perimeter to blackness within is equal on both sides. From there, pick the line width to ensure the resulting image is the right average darkness.
Ten iterations of the process are shown below, along with the starting point and reference image.