diff --git a/pic/2048merge1.tikz b/pic/2048merge1.tikz
new file mode 100644
index 0000000..cebd9a6
--- /dev/null
+++ b/pic/2048merge1.tikz
@@ -0,0 +1,54 @@
+\begin{tikzpicture}[scale=0.75,transform shape]
+    % Draw the grid
+    \foreach \i in {0,...,3} {
+        \foreach \j in {0,...,3} {
+            \draw[fill=gray!20] (\i,\j) rectangle ++(1,1);
+        }
+    }
+
+    % Draw the tiles with numbers
+    \foreach \i/\j/\n/\color in {0/0/2/20, 1/1/4/40, 2/2/8/60, 3/3/16/80, 2/3/16/80} {
+        \draw[fill=orange!\color] (\i,\j) rectangle ++(1,1);
+        \node at (\i+0.5,\j+0.5) {\textbf{\n}};
+    }
+
+    \begin{scope}[xshift=6cm]
+        \foreach \i in {0,...,3} {
+            \foreach \j in {0,...,3} {
+                \draw[fill=gray!20] (\i,\j) rectangle ++(1,1);
+            }
+        }
+
+        % Draw the tiles with numbers
+        \foreach \i/\j/\n\color in {3/0/2/20, 3/1/4/40, 3/2/8/60, 3/3/32/100} {
+            \draw[fill=orange!\color] (\i,\j) rectangle ++(1,1);
+            \node at (\i+0.5,\j+0.5) {\textbf{\n}};
+        }
+    \end{scope}
+
+    \begin{scope}[xshift=12cm]
+        \foreach \i in {0,...,3} {
+            \foreach \j in {0,...,3} {
+                \draw[fill=gray!20] (\i,\j) rectangle ++(1,1);
+            }
+        }
+
+        % Draw the tiles with numbers
+        \foreach \i/\j/\n/\color in {3/0/2/20, 3/1/4/40, 3/2/8/60, 3/3/32/100,1/0/2/20} {
+            \draw[fill=orange!\color] (\i,\j) rectangle ++(1,1);
+            \node at (\i+0.5,\j+0.5) {\textbf{\n}};
+        }
+    \end{scope}
+
+    \draw[thick, black,->] (2,4) -- (2,5) -- (8,5) -- (8,4) ;
+    \draw[thick, black,->] (8,0) -- (8,-1) -- (14,-1) -- (14,0) ;
+
+    \node at (5,4.5) {$r=32$};
+    \node at (11.5,-0.5) {random tile};
+
+    \node at (-0.5,2) {$B_1=$};
+    \node at (5.5,2) {$B_1^{'} =$};
+    \node at (11.5,2) {$B_2=$};
+
+\end{tikzpicture}
+
diff --git a/pic/2048merge2.tikz b/pic/2048merge2.tikz
new file mode 100644
index 0000000..a978a77
--- /dev/null
+++ b/pic/2048merge2.tikz
@@ -0,0 +1,53 @@
+\begin{tikzpicture}[scale=0.75,transform shape]
+    % Draw the grid
+    \foreach \i in {0,...,3} {
+        \foreach \j in {0,...,3} {
+            \draw[fill=gray!20] (\i,\j) rectangle ++(1,1);
+        }
+    }
+
+    % Draw the tiles with numbers
+    \foreach \i/\j/\n/\color in {0/0/2/20, 1/1/4/40, 2/2/8/60, 2/3/16/80, 3/3/32/100} {
+        \draw[fill=orange!\color] (\i,\j) rectangle ++(1,1);
+        \node at (\i+0.5,\j+0.5) {\textbf{\n}};
+    }
+
+    \begin{scope}[xshift=6cm]
+        \foreach \i in {0,...,3} {
+            \foreach \j in {0,...,3} {
+                \draw[fill=gray!20] (\i,\j) rectangle ++(1,1);
+            }
+        }
+
+        % Draw the tiles with numbers
+        \foreach \i/\j/\n\color in {3/0/2/20, 3/1/4/40, 3/2/8/60, 2/3/16/80,3/3/32/100} {
+            \draw[fill=orange!\color] (\i,\j) rectangle ++(1,1);
+            \node at (\i+0.5,\j+0.5) {\textbf{\n}};
+        }
+    \end{scope}
+
+    \begin{scope}[xshift=12cm]
+        \foreach \i in {0,...,3} {
+            \foreach \j in {0,...,3} {
+                \draw[fill=gray!20] (\i,\j) rectangle ++(1,1);
+            }
+        }
+
+        % Draw the tiles with numbers
+        \foreach \i/\j/\n/\color in {3/0/2/20, 3/1/4/40, 3/2/8/60, 3/3/32/100,1/0/2/20,2/3/16/80} {
+            \draw[fill=orange!\color] (\i,\j) rectangle ++(1,1);
+            \node at (\i+0.5,\j+0.5) {\textbf{\n}};
+        }
+    \end{scope}
+
+    \draw[thick, black,->] (2,4) -- (2,5) -- (8,5) -- (8,4) ;
+    \draw[thick, black,->] (8,0) -- (8,-1) -- (14,-1) -- (14,0) ;
+
+    \node at (5,4.5) {$r=0$};
+    \node at (11.5,-0.5) {random tile};
+
+    \node at (-0.5,2) {$B_1=$};
+    \node at (5.5,2) {$B_1^{'} =$};
+    \node at (11.5,2) {$B_2=$};
+
+\end{tikzpicture}
\ No newline at end of file