## Algorithm

## Recurrence plot

In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space. In bioinformatics a dot plot is a graphical method for comparing two biological sequences and identifying regions of close similarity. It is a type of recurrence plot. One way to visualize the similarity between two protein or nucleic acid sequences is to use a similarity matrix, known as a dot plot. These are two-dimensional matrices that have the sequences of the proteins being compared along the vertical and horizontal axes. For a simple visual representation of the similarity between two sequences, individual cells in the matrix can be shaded black if residues are identical, so that matching sequence segments appear as runs of diagonal lines across the matrix.

## Settings for DNA plot

The plot is the result of pattern comparison. The pattern length setting gives the length of the pattern. The first column of the matrix is the compare result of the first pattern with the consecutive comparison with each other pattern of the string.

For each pattern a twelve dimensional vector with the compnents: center, count and distance is used to define a metric.

### Center

The first four components of the vector are the center or heavy point of the letters A, C, G and T in the pattern.

### Number

The next four components are the counted number of the letters A, C, G and T in the pattern.

### Distance

The last four components are the maximal distance of the letters A, C, G and T in the pattern.

### Comparison

The length of the difference vector of the two patterns gives a value for the similarity of the patterns.

### Plot

In the color plot count, distance and center scale the colors cyan, magenta and yellow in the CMYK color room.

The gray plot uses the whole vector to define the gray value.

### 2D FFT

The gray plot is the base for 2D FFT to calculate the power spectrum and the filtered reconstruction.