A theoretical study of intersecting fold patterns

Theoretical studies show that when a thin viscous layer embedded in a viscous medium is subjected to compression in two perpendicular directions in the plane of the layer, the lengths of arc in the two directions, λ₁ and λ₂, are related by the equation: {1}/{λ ₁}² + {1}/{λ ₂}² = {1}/{λ _e}² where λ_e is the length of arc of folds which would have developed if the compression was in one direction only. If the compressions in the two directions are equal, the lengths of arc of the resulting domes and basins are √2 times that of folds which may develop by unidirectional compression. It is also found that when a set of concentric folds with semicircular cusps is compressed parallel to the fold axis, the length of arc of the later superposed folds will depend on the original radius of curvature of the concentric folds. Stretching parallel to the axis of the late folds is an essential feature in this case.