Fabrication costs eat you alive if you try to approximate a fractal too closely; but that is essentially where the later generations of solid metal heatsinks were heading before heatpipes hit the scene.
In the cheapest and simplest incarnation is just a beefy heat spreader plate on the bottom to ensure that each fin gets a reasonable connection to the heat source. In fancier versions, the spreader also extends vertically to help transfer heat to the more distant parts of the fins.
Recent AMD retail heatsinks use a clever design (cheap, because it's an aluminum extrusion with just a couple of cuts for the retention clip; but a combination of fins for surface area and bulkier conductive struts to feed the fins): image
. The central slug is about the same size as the CPU heat spreader, and is solid throughout except for the slits for the retention clip. The longest fins are the ones directly attached to it. The four thicker struts on each corner support shorter fins(longer close to the base, shortest at the edges where there will be the least heat available for dissipation).
Heatpipes are superior enough to just about any solid material(with the possible exception of diamonds and carbon nanotubes; but those aren't really options) that most of the more expensive coolers have moved to 'heatpipes as close to the CPU as possible, loads of sheet metal fins with the heatpipes running through them' design; but you can definitely see the tradeoffs between surface area and conductive cross section in today's cheaper extrusion designs and the last generation or two of pre-heatpipe enthusiast gear.