Basic Examples (3) 

Produce a triangulation of a 1+1-dimensional flat (Minkowski) spacetime into simplices of measure (area) up to 0.05:

In[1]:=

Out[1]=

Show the causal graph:

In[2]:=

Out[2]=

Show the full causal graph (without transitive reduction):

In[3]:=

Out[3]=

Show the causal graph using only triangulation edges:

In[4]:=

Out[4]=

Produce a triangulation of a 1+1-dimensional flat (Minkowski) spacetime into smaller simplices of measure (area) up to 0.01 instead:

In[5]:=

Out[5]=

Show the causal graph:

In[6]:=

Out[6]=

Show the mesh region corresponding to the triangulated spacetime surface:

In[7]:=

Out[7]=

Show the connectivity graph of this mesh region:

In[8]:=

Out[8]=

Show the full triangulated causal graph (without transitive reduction):

In[9]:=

Out[9]=

Produce a triangulation of a 2+1-dimensional flat (Minkowski) spacetime into simplices of measure (volume) up to 1:

In[10]:=

Out[10]=

Show the causal graph:

In[11]:=

Out[11]=

Show the pure causal graph (with vertex coordinate information removed):

In[12]:=

Out[12]=

Show only the pure triangulated causal graph (with vertex coordinate information removed):

In[13]:=

Out[13]=

Scope (5) 

Triangulations can be produced for 0+1-dimensional spacetimes:

In[14]:=

Out[14]=

Show the pure causal graph:

In[15]:=

Out[15]=

Produce a triangulation of a 1+1-dimensional spacetime:

In[16]:=

Out[16]=

Show the pure causal graph:

In[17]:=

Out[17]=

Produce a triangulation of a 2+1-dimensional spacetime:

In[18]:=

Out[18]=

Show the pure causal graph:

In[19]:=

Out[19]=

Properties can be requested directly from FlatSpacetimeTriangulation:

In[20]:=

Out[20]=

Produce a triangulation of a 1+1-dimensional flat (Minkowski) spacetime into simplices of measure (area) up to 0.005:

In[21]:=

Out[21]=

Show the complete list of properties:

In[22]:=

Out[22]=

Show the full causal graph:

In[23]:=

Out[23]=

Show the transitively-reduced causal graph:

In[24]:=

Out[24]=

Show the full causal graph using only triangulation edges:

In[25]:=

Out[25]=

Show the transitively-reduced causal graph using only triangulation edges:

In[26]:=

Out[26]=

Plot the positions of the points in the triangulation only (without causal edges):

In[27]:=

Out[27]=

Show a complete list of spacetime coordinates for the points in the triangulation (the last coordinate is always the time coordinate):

In[28]:=

Out[28]=

Show the number of points in the triangulation:

In[29]:=

Out[29]=

Show the number of dimensions in the background spacetime:

In[30]:=

Out[30]=

Show the first 50 (undirected) edges in the triangulation of the spacetime surface:

In[31]:=

Out[31]=

Show the total number of (undirected) edges in the triangulation of the spacetime surface:

In[32]:=

Out[32]=

Show the maximum measure (in this case, area) of the simplices in the triangulation:

In[33]:=

Out[33]=

Show the total number of causal edges:

In[34]:=

Out[34]=

Show the number of causal edges after transitive reduction:

In[35]:=

Out[35]=

Show the total number of causal edges appearing in the triangulation:

In[36]:=

Out[36]=

Show the number of causal edges appearing in the triangulation after transitive reduction:

In[37]:=

Out[37]=

Show the pure full causal graph (with vertex coordinate information removed):

In[38]:=

Out[38]=

Show the pure transitively-reduced causal graph (with vertex coordinate information removed):

In[39]:=

Out[39]=

Show the pure full causal graph using only triangulation edges (with vertex coordinate information removed):

In[40]:=

Out[40]=

Show the pure transitively-reduced causal graph using only triangulation edges (with vertex coordinate information removed):

In[41]:=

Out[41]=

Show the mesh region corresponding to the triangulated spacetime surface:

In[42]:=

Out[42]=

Show the connectivity graph of this mesh region:

In[43]:=

Out[43]=