## 3 Experimental Results
### Complementary Cumulative Histograms of Freeze Length  
Figure 10 shows the CCHs of freeze length observed in the experiments accumulated over the four quadrants. A log-linear presentation is used which is beneficial in revealing exponential and geometric progressions. For small freeze lengths in the range \(1\leq x\leq 6\), the CCHs drop with a similar gradient irrespective of the considered distances. In particular, the linearly decreasing progression of the CCHs for this range of small freeze length indicates an exponential or geometric decay. For medium freeze lengths in the range \(7\leq x\leq 40\), the CCHs also drop approximately exponentially or geometrically but with different gradients depending on the selected distance. The steepest slope and least steep slope are obtained for the distances \(d=10\,\mathrm{m}\) and \(d=12.5\,\mathrm{m}\), respectively. For large freeze lengths in the range \(41\leq x\), tails develop in the CCHs for \(d=12.5\,\mathrm{m}\), and \(d=15\,\mathrm{m}\) which are due to single occurrences of long freezes. The above finding about the progression of the CCHs of freeze length being generally comprised of three parts can be explored in the derivation of statistical models including exponential and geometric distributions (see Section 4).  
Figure 11 shows the quadrant-specific CCHs of freeze length. It is observed that the quadrants Q1 and Q2 facing the glass wall of the multi-purpose lecture hall experience similar CCHs of freeze length with short tails at most. On the other hand, the quadrants Q3 and Q4 facing the wall mainly composed of wooden panels encounter CCHs of freeze length with well developed tails. In particular, the following CCH progressions are observed:  
* **Q1:** Similar exponential progressions are observed for distances \(d=10\,\mathrm{m}\) and \(d=12.5\,\mathrm{m}\) and an exponential progression with a short tail induced by a single freeze event is observed for distance \(d=15\,\mathrm{m}\). Because the freeze lengths are positive integers, it should be noted that the exponential progressions can be described equivalently as geometric progressions (see Section 4).
* **Q2:** The CCHs of freeze length show an exponential (or geometric) progression without a tail for all distances.
* **Q3:** Exponential (or geometric) progressions are observed for all distances with a transition region with different slopes developing for distances \(d=12.5\,\mathrm{m}\) and \(d=15\,\mathrm{m}\) along with tails due to a single freeze occurrence.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(d\) [m] & Mean & Median & Mode & SD & Skewness & Kurtosis \\ \hline
10 & 5.0737 & 5 & 3 & 2.2467 & 0.6938 & 0.1249 \\
12.5 & 7.0909 & 5 & 4 & 6.0678 & 3.1341 & 13.8458 \\
15 & 6.3659 & 5 & 3 & 5.8159 & 4.1254 & 24.8990 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measures of central tendency of freeze lengths in number of frames.  
Figure 10: CCH of freeze length accumulated over the four quadrants.  
* **Q4:** An exponential (or geometric) progression of the CCH is observed for the case of \(d=10\,\mathrm{m}\) without a tail while exponential (or geometric) progressions are observed for \(d=12.5\,\mathrm{m}\) and \(d=15\,\mathrm{m}\) accompanied with a small tail and a large tail, respectively, caused by a single freeze occurrence.  
In summary, the quadrant-specific CCHs of freeze length span a range of exponential (or geometric) progressions with and without tails depending on the particular quadrant and distance. Apart from similar shifts observed in the respective quadrants, similar initial drops by one order of magnitude can be seen until the freeze length reaches \(x=10\). These results also indicate the dominance of the contribution of Q3 and Q4 to the CCHs in Figure 10 for freeze length \(x\geq 10\).