The columnar morphologies commonly found in all vapor‐deposited thin films prepared under low mobility conditions have been classified by several variations of what have been termed structure zone models. Such morphological structures are found to have a strong similarity in shape and form over six orders of magnitude in film thickness and three orders of magnitude in magnification for films of a given thickness. Thick (45‐mm) pyrolytic graphite films are shown to be a good demonstration of the continuous growth evolution of conical‐shaped units. Due to competition for growth each cone eventually goes through a death stage. A model based upon these general structural observations is presented and is shown to be a geometric construction similar to a Sierpinski gasket. The origin of this morphology seems to be the natural clustering which occurs due to the random process of ballistic aggregation.