α=.05;
Δt=.01;
Δx=.25;
λ=((α*Δt)/((Δx)^2));
ϵ=10^-5;

a=SparseArray[{i_,j_}/;j-1≤i≤j+1->λ,{4,4},0]+(1-3λ)*IdentityMatrix[4];

record={};
state={.075,.075,.025,.025}
next=a.state;
record=Append[record,state];
While[Abs[next[[3]]-state[[3]]]>ϵ,
state=next;
next=a.state;
record=Append[record,state];
]

ListPlot3D[record]

ListPointPlot3D[record]

α=.05;
Δt=.01;
Δx=.25;
λ=((α*Δt)/((Δx)^2));
ϵ=10^-5;
n=2;

a=SparseArray[{i_,j_}/;j-1≤i≤j+1->λ,{4*n,4*n},0]+(1-3λ)*IdentityMatrix[4*n];

record={};
state=Join[Table[.075,{i,1,2*n}],Table[.025,{i,2*n+1,4*n}]]
next=a.state;
record=Append[record,state];
While[Abs[next[[2*n]]-state[[2*n]]]>ϵ,
state=next;
next=a.state;
record=Append[record,state];
]

ListPlot3D[record]

ListPointPlot3D[record]