diff --git a/Makefile b/Makefile
index 9b704d54..5ce97aad 100644
--- a/Makefile
+++ b/Makefile
@@ -4,6 +4,7 @@ IMPLEMENTATION_FILES = $(shell find -name '*.ml')
 
 TARGETS_LIB = containers.cmxa containers.cma
 TARGET_THREAD_LIB = thread_containers.cmxa thread_containers.cma
+EXAMPLES = examples/mem_size.native examples/collatz.native
 OPTIONS = -use-ocamlfind
 
 all: lib lib_thread
@@ -14,8 +15,8 @@ lib:
 lib_thread:
 	ocamlbuild $(OPTIONS) $(TARGETS_LIB) $(TARGET_THREAD_LIB)
 
-examples:
-	ocamlbuild $(OPTIONS) -I . examples/mem_size.native
+examples: all
+	ocamlbuild $(OPTIONS) -I . $(EXAMPLES)
 
 tests:
 	ocamlbuild $(OPTIONS) -package oUnit -I . tests/run_tests.native
diff --git a/examples/collatz.ml b/examples/collatz.ml
new file mode 100644
index 00000000..47b78aea
--- /dev/null
+++ b/examples/collatz.ml
@@ -0,0 +1,20 @@
+
+(** Display the graph of the collatz conjecture, starting from the given int *)
+
+let g = LazyGraph.map
+  ~edges:(fun () -> [])
+  ~vertices:(fun i -> [`Label (string_of_int i)])
+  LazyGraph.collatz_graph
+
+let collatz n filename =
+  Format.printf "print graph to %s@." filename;
+  let out = open_out filename in
+  let fmt = Format.formatter_of_out_channel out in
+  LazyGraph.Dot.pp ~name:"collatz" g fmt (Enum.singleton n);
+  Format.pp_print_flush fmt ();
+  close_out out
+
+let _ =
+  if Array.length Sys.argv < 3
+    then (Format.printf "use: collatz num file@."; exit 0)
+    else collatz (int_of_string Sys.argv.(1)) Sys.argv.(2)
diff --git a/lazyGraph.ml b/lazyGraph.ml
index 6d81470d..fbbe49a1 100644
--- a/lazyGraph.ml
+++ b/lazyGraph.ml
@@ -390,3 +390,29 @@ module Dot = struct
     let enum = Full.bfs_full graph vertices in
     pp_enum ~eq:graph.eq ~hash:graph.hash ~name formatter enum
 end
+
+(** {2 Example of graphs} *)
+
+let divisors_graph =
+  let rec divisors acc j i =
+    if j = i then acc
+    else
+      let acc' = if (i mod j = 0) then j :: acc else acc in
+      divisors acc' (j+1) i
+  in
+  let force i =
+    if i > 2
+      then
+        let l = divisors [] 2 i in
+        let edges = Enum.map (fun i -> (), i) (Enum.of_list l) in
+        Node (i, i, edges)
+      else
+        Node (i, i, Enum.empty)
+  in make force
+
+let collatz_graph =
+  let force i =
+    if i mod 2 = 0
+      then Node (i, i, Enum.singleton ((), i / 2))
+      else Node (i, i, Enum.singleton ((), i * 3 + 1))
+  in make force
diff --git a/lazyGraph.mli b/lazyGraph.mli
index 893999b7..744f7db5 100644
--- a/lazyGraph.mli
+++ b/lazyGraph.mli
@@ -207,3 +207,9 @@ module Dot : sig
     (** Pretty print the given graph (starting from the given set of vertices)
         to the channel in DOT format *)
 end
+
+(** {2 Example of graphs} *)
+
+val divisors_graph : (int, int, unit) t
+
+val collatz_graph : (int, int, unit) t