Fractals and Hidden Symmetries in DNA

Table 1

$\{Y_0,Y_1{,\dots ,Y}_p\}\oplus \{Y_{p+1},Y_{p+2}{,\dots ,Y}_{2p}\}\oplus \cdots$	Complex values sequence
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$x_i=\Re (Y_i),\mathrm{\hspace{0.17em}\hspace{0.17em}}{y}_i=\Im (Y_i)$	Real values sequences
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$\begin{array}{c}\{x_0,x_1{,\dots ,x}_p\}\oplus \{x_{p+1},x_{p+2}{,\dots ,x}_{2p}\}\oplus \cdots \\ \{y_0,y_1{,\dots ,y}_p\}\oplus \{y_{p+1},y_{p+2}{,\dots ,y}_{2p}\}\oplus \cdots \end{array}\rangle$	Real sequences
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$\begin{array}{c}{𝒲}^p\{x_0,x_1{,\dots ,x}_p\}\oplus {𝒲}^p\{x_{p+1},x_{p+2}{,\dots ,x}_{2p}\}\oplus \cdots \\ {𝒲}^p\{y_0,y_1{,\dots ,y}_p\}\oplus {𝒲}^p\{y_{p+1},y_{p+2}{,\dots ,y}_{2p}\}\oplus \cdots \end{array}\rangle$	Wavelet transform
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$\begin{array}{c}{\{\alpha ,{\beta }_0^0,{\beta }_0^1,{\beta }_1^1,\dots \}}_1\oplus {\{\alpha ,{\beta }_0^0,{\beta }_0^1,{\beta }_1^1,\dots \}}_2\oplus \cdots \\ {\{{\alpha }^{*},{\beta }_0^{*0},{\beta }_0^{*1},{\beta }_1^{*1},\dots \}}_1\oplus {\{{\alpha }^{*},{\beta }_0^{*0},{\beta }_0^{*1},{\beta }_1^{*1},\dots \}}_2\oplus \cdots \end{array}\rangle$	Wavelet coefficients
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$\begin{array}{c}{\{(\alpha ,{\alpha }^{*})\}}_1\oplus {\{(\alpha ,{\alpha }^{*})\}}_2\oplus {\{(\alpha ,{\alpha }^{*})\}}_3\cdots \\ {\{({\beta }_0^0,{\beta }_0^{*0})\}}_1\oplus {\{({\beta }_0^0,{\beta }_0^{*0})\}}_2\oplus {\{({\beta }_0^0,{\beta }_0^{*0})\}}_3\cdots \\ {\{({\beta }_0^1,{\beta }_0^{*1})\}}_1\oplus {\{({\beta }_0^1,{\beta }_0^{*1})\}}_2\oplus {\{({\beta }_0^1,{\beta }_0^{*1})\}}_3\cdots \end{array}\rangle$	Clusters
$⋮\hspace{1em}⋮\hspace{1em}⋮$