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Local and fast structural probes using synchrotron radiation have shownnanoscale striped puddles and nanoscale phase separation in dopedperovskites.It is known that the striped phases in doped perovskites are due tocompeting interactions involving charge, spin and lattice degrees offreedom,but while many theoretical models for spin and charge stripes have beenproposed we are missing theoretical models describing the complex latticestriped modulations in doped perovskites. In this work we show that twodifferent stripes can be represented as a superposition of a pair of stripes,U(theta_n) and D(theta_n), characterized by perovskite tilts where one of thepair is rotated in relation to the other partner by an angle Delta(theta_n)=pi/2. The spatial distribution of the U and D stripes is reduced to allpossible maps in the well-known mathematical four-color theorem. Both theperiodic striped puddles and random structures can be represented by using$planar$ graphs with a chromatic number. To observe the colors in mappingexperiments, it is necessary to recover variously oriented tilting effects fromthe replica. It is established that there is an interplay between theannihilation/creation of new stripes and ordering/disordering tilts in relationto the theta _n angle in the CuO2 plane, where the characteristic shape of thestripes coincides with the tilting-ordered regions. By their origin, theboundaries between the stripes should be atomically sharp.

Is there any hidden symmetry in the stripe structure of perovskite high temperature superconductors?