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New results on mean orientation of the terrain elements of different scales (sizes) are presented alongside with a summary of previous investigations. Analysis of a selection of regions shows that the transition to certain “special” scales has above average frequency of jump changes in relief orientation. These special scales are detected in varying regions and when analyzing large sections (up to one quarter) of the Earth’s surface. What happens with the terrain pattern on those scales is examined in details looking at valleys that have different widths. All the results are obtained by utilizing LESSA technology (Lineament Extraction and Stripe Statistical Analysis). LESSA automatically detects position and orientation of the valley axis and calculates its mean direction in a sliding window. Using SRTM (Shuttle radar topographic mission) data, about 30 different parts of the Earth land were analyzed in a wide range of scales. A hypothesis is presented about the existence of a valley hierarchy with statistically quantified valley widths. This hypothesis allows explaining the above-mentioned special scales. Those special scales in turn allow detecting width ranges of the valleys on different levels of the hierarchy. The geometric sequence that sets the center of those ranges is presented. The presented hypothesis is associated with Horton’s laws