All Figures

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{H3893F1.eps}\end{figure}$ Figure 1: An image made by a regular distribution of randomly oriented U, and including two structures, the former consisting of U letters uniformly oriented, the latter of randomly oriented T. of the two structures only one is easily visible (adapted from Legrenzi 2002).
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{H3893F2.eps}\end{figure}$ Figure 2: H'(m) versus m for a pseudorandom distribution of approx. 4000 black pixels. H' has been averaged over an ensemble of 100 different configurations.
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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{H3893F3.eps}\end{figure}$ Figure 3: A pseudorandom uniform distribution of $m_{\rm s} \times m_{\rm s}$ square structures (with $m_{\rm s} = 7$ ) around the sites of a square lattice with a lattice constant $m_{\rm r} = 20$ pixels. We remark that each structure is distributed inside the square cell centred on each lattice site.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F4.eps}\end{figure}$ Figure 4: The normalised information entropy H' (empty squares) relative to the pattern reported in Fig. 3. Solid lines refer to the single contributions derived by fitting H' using Eq. (7) with k=4.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F5.eps} \end{figure}$ Figure 5: The peak positions m_k derived from the decomposition of H' plotted versus odd numbers. The solid line is a linear best fit using Eq. (7). The resulting lattice constant is $m_{\rm r} = [20.0 \pm 0.2]$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F6.eps}\end{figure}$ Figure 6: The THEMIS average intensity (left panel) and rms (right panel) field as obtained by the 40 min time-series. The image size is $\approx$ $27 \hbox {$^{\prime \prime }$ }\times 27 \hbox {$^{\prime \prime }$ }$ as resulting after $k-\omega$ filtering.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F7.eps}\end{figure}$ Figure 7: The DST average intensity (left panel) and rms (right panel) field as obtained by the 90 min time-series. The image size is a portion of $\approx$ $27 \hbox {$^{\prime \prime }$ }\times 27 \hbox {$^{\prime \prime }$ }$ of the original image.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{H3893F8.eps}\end{figure}$ Figure 8: The binarized images of THEMIS (left panel) and DST (right panel) average intensity field reported in Fig. 6 and 7. Images size is $27 \hbox {$^{\prime \prime }$ }\times 27 \hbox {$^{\prime \prime }$ }$ for convenience.
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In the text

$\begin{figure} \par\includegraphics[width=16.4cm,clip]{H3893F9.eps}\end{figure}$ Figure 9: The normalised information entropy H' at different times for the THEMIS binarized intensity fields.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F10.eps}\end{figure}$ Figure 10: The behaviour of the reduced $\chi ^2_{\rm r}(n)$ versus the number n of contributions in the case of THEMIS H'(r) decomposition. The dashed line is an eye guide.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F11.eps}\par\includegraphics[width=8.8cm,clip]{H3893F12.eps}\end{figure}$ Figure 11: The decomposition of the normalised information entropy H' for two images in the case of THEMIS (upper panel) and DST (lower panel), respectively. Solid line is the best fit using Eq. (7). The dashed lines show the single contributions.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F13.eps}\par\includegraphics[width=8.8cm,clip]{H3893F14.eps}\end{figure}$ Figure 12: The behaviour of the position of the contributions of the H'(r) decomposition for THEMIS (upper panel) and DST (lower panel), respectively.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F15.eps}\end{figure}$ Figure 13: The average positions of the peaks of the H'(r) decompositions on single images for THEMIS (black circles) and DST (empty circles) observations. Error bar represents the standard deviation. The solid and dashed lines are linear best fits using the expression Eq. (8) of Sect. 2.
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{H3893F16.eps}\end{figure}$ Figure 14: The persistency pattern for the granulation field as evaluated from DST binarized images. The upper panel shows a 3-d view of this pattern where the multipeaked structure is clearly evident. The lower panel shows a 2-d view of the same persistence pattern where only the part of the signal that exceeds the RMS value is shown.
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In the text

$\begin{figure} \par\includegraphics[width=16.4cm,clip]{H3893F17.eps}\end{figure}$ Figure 15: The evolution of the normalised information entropy H' by averaging DST images with time.
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In the text

$\begin{figure} \includegraphics[width=8.8cm,clip]{H3893F18.eps}\end{figure}$ Figure 16: Percetange contribution to the overall information entropy H'(r) in three different range of scales $\Delta r$ as a function of averaging time $\Delta t$ .
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In the text

$\begin{figure} \includegraphics[width=8.8cm,clip]{H3893F19.eps}\end{figure}$ Figure 17: The normalised information entropy H' (empty circles) for the DST binarized average intensity field. Solid line is the best fit using Eq. (7) with k=6. The dotted lines show the single contributions. Only contributions with maxima inside 10 Mm are shown for convenience.
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In the text

$\begin{figure} \includegraphics[width=8.8cm,clip]{H3893F20.eps}\end{figure}$ Figure 18: The peak positions of the H'(r) contributions versus odd numbers for THEMIS (solid circles) and DST (empty circles) average intensity fileds. The solid and dashed lines are linear fit for THEMIS and DST, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F21.eps}\end{figure}$ Figure A.1: Two periodic patterns of structures: a square lattice (left panel) and a triangular lattice (right panel).

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F22.eps} \includegraphics[width=8.8cm,clip]{H3893F23.eps}\end{figure}$ Figure A.2: The normalised information entropy H'(m) of the two patterns reported in Fig. A.1. Upper and lower panel refer to the square and triangular lattice, respectively.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F24.eps} \end{figure}$ Figure A.3: Two periodic patterns of structures: a square lattice (left panel) and a triangular lattice (right panel).

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F25.eps} \includegraphics[width=8.8cm,clip]{H3893F26.eps}\end{figure}$ Figure A.4: The H'(m) behaviour for the two random patterns reported in Fig. A.3. Upper and lower panels refer to triangular and square lattice. Solid line is the best fit of H' using Eq. (7). Dashed lines are the single contributions.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F27.eps}\end{figure}$ Figure A.5: The trends of the peak positions versus the odd numbers for the two decompositions shown in Fig. A.4. Empty and solid circles indicate the peak positions for the triangular and square lattice, respectively. Solid and dashed lines are linear best fits.

In the text

$\begin{figure} \par\includegraphics[width=4.4cm,clip]{H3893F28.eps}\end{figure}$ Figure A.6: A snapshot of a pseudorandom pattern of non-overlapping structures.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F29.eps}\end{figure}$ Figure A.7: H'(m) for the single snapshot reported in Fig. A.6 (solid circles) and the set of 1000 pseudorandom patterns (empty circles).

In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{H3893F1.eps}\end{figure}$	Figure 1: An image made by a regular distribution of randomly oriented U, and including two structures, the former consisting of U letters uniformly oriented, the latter of randomly oriented T. of the two structures only one is easily visible (adapted from Legrenzi 2002).
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{H3893F2.eps}\end{figure}$	Figure 2: H'(m) versus m for a pseudorandom distribution of approx. 4000 black pixels. H' has been averaged over an ensemble of 100 different configurations.
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$\begin{figure} \par\includegraphics[width=4.3cm,clip]{H3893F3.eps}\end{figure}$	Figure 3: A pseudorandom uniform distribution of $m_{\rm s} \times m_{\rm s}$ square structures (with $m_{\rm s} = 7$ ) around the sites of a square lattice with a lattice constant $m_{\rm r} = 20$ pixels. We remark that each structure is distributed inside the square cell centred on each lattice site.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F4.eps}\end{figure}$	Figure 4: The normalised information entropy H' (empty squares) relative to the pattern reported in Fig. 3. Solid lines refer to the single contributions derived by fitting H' using Eq. (7) with k=4.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F5.eps} \end{figure}$	Figure 5: The peak positions m_k derived from the decomposition of H' plotted versus odd numbers. The solid line is a linear best fit using Eq. (7). The resulting lattice constant is $m_{\rm r} = [20.0 \pm 0.2]$ .
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F6.eps}\end{figure}$	Figure 6: The THEMIS average intensity (left panel) and rms (right panel) field as obtained by the 40 min time-series. The image size is $\approx$ $27 \hbox {$^{\prime \prime }$ }\times 27 \hbox {$^{\prime \prime }$ }$ as resulting after $k-\omega$ filtering.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F7.eps}\end{figure}$	Figure 7: The DST average intensity (left panel) and rms (right panel) field as obtained by the 90 min time-series. The image size is a portion of $\approx$ $27 \hbox {$^{\prime \prime }$ }\times 27 \hbox {$^{\prime \prime }$ }$ of the original image.
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{H3893F8.eps}\end{figure}$	Figure 8: The binarized images of THEMIS (left panel) and DST (right panel) average intensity field reported in Fig. 6 and 7. Images size is $27 \hbox {$^{\prime \prime }$ }\times 27 \hbox {$^{\prime \prime }$ }$ for convenience.
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$\begin{figure} \par\includegraphics[width=16.4cm,clip]{H3893F9.eps}\end{figure}$	Figure 9: The normalised information entropy H' at different times for the THEMIS binarized intensity fields.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F10.eps}\end{figure}$	Figure 10: The behaviour of the reduced $\chi ^2_{\rm r}(n)$ versus the number n of contributions in the case of THEMIS H'(r) decomposition. The dashed line is an eye guide.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F11.eps}\par\includegraphics[width=8.8cm,clip]{H3893F12.eps}\end{figure}$	Figure 11: The decomposition of the normalised information entropy H' for two images in the case of THEMIS (upper panel) and DST (lower panel), respectively. Solid line is the best fit using Eq. (7). The dashed lines show the single contributions.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F13.eps}\par\includegraphics[width=8.8cm,clip]{H3893F14.eps}\end{figure}$	Figure 12: The behaviour of the position of the contributions of the H'(r) decomposition for THEMIS (upper panel) and DST (lower panel), respectively.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3893F15.eps}\end{figure}$	Figure 13: The average positions of the peaks of the H'(r) decompositions on single images for THEMIS (black circles) and DST (empty circles) observations. Error bar represents the standard deviation. The solid and dashed lines are linear best fits using the expression Eq. (8) of Sect. 2.
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$\begin{figure} \par\includegraphics[width=6.4cm,clip]{H3893F16.eps}\end{figure}$	Figure 14: The persistency pattern for the granulation field as evaluated from DST binarized images. The upper panel shows a 3-d view of this pattern where the multipeaked structure is clearly evident. The lower panel shows a 2-d view of the same persistence pattern where only the part of the signal that exceeds the RMS value is shown.
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$\begin{figure} \par\includegraphics[width=16.4cm,clip]{H3893F17.eps}\end{figure}$	Figure 15: The evolution of the normalised information entropy H' by averaging DST images with time.
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$\begin{figure} \includegraphics[width=8.8cm,clip]{H3893F18.eps}\end{figure}$	Figure 16: Percetange contribution to the overall information entropy H'(r) in three different range of scales $\Delta r$ as a function of averaging time $\Delta t$ .
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$\begin{figure} \includegraphics[width=8.8cm,clip]{H3893F19.eps}\end{figure}$	Figure 17: The normalised information entropy H' (empty circles) for the DST binarized average intensity field. Solid line is the best fit using Eq. (7) with k=6. The dotted lines show the single contributions. Only contributions with maxima inside 10 Mm are shown for convenience.
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$\begin{figure} \includegraphics[width=8.8cm,clip]{H3893F20.eps}\end{figure}$	Figure 18: The peak positions of the H'(r) contributions versus odd numbers for THEMIS (solid circles) and DST (empty circles) average intensity fileds. The solid and dashed lines are linear fit for THEMIS and DST, respectively.
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