The issue of migration among the rural population living on the lands of the Czech Crown in the early modern age continues to attract only marginal attention in Czech historiography. Therefore, those people who lived on the very edge of that society remain outside the scope of research interest. The Romany Gypsies who were bom without homes, lie also outside the traditional focus of attention. In the early modern age, anyone could kill a Romany Gypsy without punishment; people were meant to despise them and were even supposed to persecute them. The Romany Gypsies were therefore forced to develop a specific strategy of action, which was intended to help them survive, and a significant role in this strategy was played by migration. A condition for survival was not only the need to maintain a strong internal structure within the Romany Gypsy group, but also the need to create ties with a settled society. These ties ensured, in the case of a threat, at least some form of a rudimentary protective social network. Such ties were probably passed down from generation to generation and the Romany Gypsies therefore, as much as was possible, restricted their movements to only well-known areas. On their travels through the landscape they tried to obtain food not only through begging and theft, but also by telling fortunes and reading palms, skilfully taking advantage of the fact that in the eyes of the settled population their lives were cloaked in mystery. However, they never forgot to emphasise their ties to the land in which they were bom and the impossibility of leaving it for another land. A question remains for further research as to whether they were persecuted for their ethnic origin or whether it was because of their nomadic lifestyle, which enabled them to evade the mechanisms of social control.
The classical self-similar fractals can be obtained as fixed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure is a (normal) space of homogeneous type. But the doubling property along this iteration is generally not preserved even when the starting point, and of course the limit point, both have the doubling property. We prove that the elements of Hutchinson orbits possess the doubling property except perhaps for radii which decrease to zero as the step of the iteration grows, and in this sense, we say that the doubling property of the limit is achieved gradually. We use this result to prove the uniform upper doubling property of the orbits.