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We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a life-threatening cardiac arrhythmia occurs; thereby facilitating a possible prediction of such an event. A comparison to the previous applied methods from symbolic dynamics and the finite-time growth rates is given.