Tupper's self-referential formula: An example

Tupper’s inequality is

  \begin{equation} \frac{1}{2} < \Bigl \lfloor mod\left(\Bigl \lfloor \frac{y}{17}\Bigr \rfloor 2^{-17\lfloor x \rfloor - mod(\lfloor y \rfloor , 17)},2\right)\Bigr \rfloor .\end{equation}   (1)

Let’s see if it holds for $x=0$ and $y=103$

Firstly, we have

  \[ \Bigl \lfloor \frac{y}{17} \Bigr \rfloor = \Bigl \lfloor \frac{103}{17} \Bigr \rfloor = \Bigl \lfloor 6.06 \Bigr \rfloor = 6. \]    

Secondly, we have

  \[ 17\lfloor x \rfloor = 17\lfloor 0 \rfloor = 0. \]    

We also have

  \[ mod(\lfloor y \rfloor , 17) = mod(\lfloor 103 \rfloor , 17) = mod(103, 17) =1. \]    

Putting all this together gives

  \[ \Bigl \lfloor mod\left(\Bigl \lfloor \frac{y}{17}\Bigr \rfloor 2^{-17\lfloor x \rfloor - mod(\lfloor y \rfloor , 17)},2\right)\Bigr \rfloor = \Bigl \lfloor mod\left(6 \times 2^{0 - 1}, 2 \right)\Bigr \rfloor =\Bigl \lfloor mod\left(\frac{6}{2}, 2 \right)\Bigr \rfloor = \Bigl \lfloor mod\left(3, 2 \right)\Bigr \rfloor = 1. \]    

Since $\frac{1}{2}<1$ the inequality holds for $x=0$ and $y=103$. Therefore, the square with coordinates $(0,103)$ should be coloured. Can you work out whether the square below, which has coordinates $(0,102)$, should be coloured?

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