Given an exisiting configuration of the volumes. one selects a volume, which then will become the reference volume. all the other volumes in the configuration are now interpretated as instances of this reference volume, which has been moved and scaled in 3dspace.
so every instance consists the reference volume plus a transformation matrix ( translation, rotation, scaling ). this forms the axiom. every occurance of the reference volume in the axiom is replaced by the axiom itself ( original volume plus all transformed instances ). all these transformation matrixes are further inherited to the next step during the process. the effect of this is an amplification of the whole structure's deformations . this continuously repeated process creates a perpetually growing geometry, but which still contains the original parameters and transformations.


number of iterations: 1 2 3

following example was generated using a standard cube with equal sides instead of the central cube

number of iterations: 1 2 3

In the following example the left cube ( Haus Wittgensteins dining room ) was selected as the reference volume .
number of iterations: 1 2 3


x1 ... xn transformation matrix ( translation, rotation, scale )


x1(x1v-x2v-..-xnv)- x2(x1v-x2v-..-xnv)-..- xn(x1v-x2v-..-xnv)

x1(x1(x1v-x2v-..-xnv)-x2(x1v-x2v-..xnv)-...-xn(x1v-x2v-..-xnv))- x2(x1(x1v-x2v-..-xnv)-x2(x1v-x2v-..xnv)-...-xn(x1v-x2v-..-xnv))-..- xn(x1(x1v-x2v-..-xnv)-x2(x1v-x2v-..xnv)-...-xn(x1v-x2v-..-xnv))