diff --git a/apps/ir_spam1/ir_spam1.c b/apps/ir_spam1/ir_spam1.c
index 1f8fe4e..2b36ac2 100644
--- a/apps/ir_spam1/ir_spam1.c
+++ b/apps/ir_spam1/ir_spam1.c
@@ -40,7 +40,7 @@ int main (void)
             ticks = 0;
             ir_uart_putc ('2');
         }
-
+x
         tinygl_update ();
     }
 
diff --git a/apps/stars1/stars1.c b/apps/stars1/stars1.c
index 0042147..3dc8c71 100644
--- a/apps/stars1/stars1.c
+++ b/apps/stars1/stars1.c
@@ -32,14 +32,13 @@
 int main (void)
 {
     uint16_t twinkle_tick = 0;
-    uint16_t create_tick = 0;
     uint8_t pwm_tick = 0;
     uint8_t i;
     uint8_t x;
     uint8_t y;
     uint8_t col;
     /* This stores the current luminance level for each pixel.  */
-    uint8_t display[TINYGL_HEIGHT][TINYGL_WIDTH] = {0, };
+    uint8_t display[TINYGL_HEIGHT][TINYGL_WIDTH] = {{0, }};
     /* This controls the luminance levels.  The maximum value
        of LUMINANCE_STEPS gives 100 percent duty cycle.   */
     const uint8_t levels[] = {0, 1, 2, 4, 8, 15, 25, 15, 8, 4, 2, 1};
@@ -78,7 +77,7 @@ int main (void)
         {
             twinkle_tick = 0;
 
-            /* Change luminance of stars until they die.  */
+            /* Vary luminance of stars.  */
             for (x = 0; x < TINYGL_WIDTH; x++)
             {
                 for (y = 0; y < TINYGL_HEIGHT; y++)
diff --git a/apps/stars3/Makefile b/apps/stars3/Makefile
new file mode 100644
index 0000000..44842fa
--- /dev/null
+++ b/apps/stars3/Makefile
@@ -0,0 +1,71 @@
+# File:   Makefile
+# Author: M. P. Hayes, UCECE
+# Date:   12 Sep 2010
+# Descr:  Makefile for stars3
+
+# Definitions.
+CC = avr-gcc
+CFLAGS = -mmcu=atmega32u2 -Os -Wall -Wstrict-prototypes -Wextra -g -I../../drivers/avr -I../../drivers -I../../utils
+OBJCOPY = avr-objcopy
+SIZE = avr-size
+DEL = rm
+
+
+# Default target.
+all: stars3.out
+
+
+# Compile: create object files from C source files.
+stars3.o: stars3.c ../../drivers/avr/system.h ../../drivers/display.h ../../utils/font.h ../../utils/pacer.h ../../utils/tinygl.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+pio.o: ../../drivers/avr/pio.c ../../drivers/avr/pio.h ../../drivers/avr/system.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+system.o: ../../drivers/avr/system.c ../../drivers/avr/system.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+timer.o: ../../drivers/avr/timer.c ../../drivers/avr/system.h ../../drivers/avr/timer.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+display.o: ../../drivers/display.c ../../drivers/avr/system.h ../../drivers/display.h ../../drivers/ledmat.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+ledmat.o: ../../drivers/ledmat.c ../../drivers/avr/pio.h ../../drivers/avr/system.h ../../drivers/ledmat.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+font.o: ../../utils/font.c ../../drivers/avr/system.h ../../utils/font.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+pacer.o: ../../utils/pacer.c ../../drivers/avr/system.h ../../drivers/avr/timer.h ../../utils/pacer.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+tinygl.o: ../../utils/tinygl.c ../../drivers/avr/system.h ../../drivers/display.h ../../utils/font.h ../../utils/tinygl.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+
+
+
+# Link: create output file (executable) from object files.
+stars3.out: stars3.o pio.o system.o timer.o display.o ledmat.o font.o pacer.o tinygl.o
+	$(CC) $(CFLAGS) $^ -o $@ -lm
+	$(SIZE) $@
+
+
+# Create hex file for programming from executable file.
+stars3.hex: stars3.out
+	$(OBJCOPY) -O ihex stars3.out stars3.hex
+
+
+# Target: clean project.
+.PHONY: clean
+clean: 
+	-$(DEL) *.o *.out *.hex
+
+
+# Target: program project.
+.PHONY: program
+program: stars3.hex
+	dfu-programmer atmega32u2 erase; dfu-programmer atmega32u2 flash stars3.hex; dfu-programmer atmega32u2 start
+
+
diff --git a/apps/stars3/Makefile.test b/apps/stars3/Makefile.test
new file mode 100644
index 0000000..e2aa9e7
--- /dev/null
+++ b/apps/stars3/Makefile.test
@@ -0,0 +1,61 @@
+# File:   Makefile
+# Author: M. P. Hayes, UCECE
+# Date:   11 Sep 2010
+# Descr:  Makefile for stars3
+
+CC = gcc
+CFLAGS = -Wall -Wstrict-prototypes -Wextra -g -I../../drivers/test -I../../drivers -I../../utils
+
+DEL = rm
+
+
+# Default target.
+all: stars3
+
+
+# Compile: create object files from C source files.
+stars3-test.o: stars3.c ../../drivers/display.h ../../drivers/test/system.h ../../utils/font.h ../../utils/pacer.h ../../utils/tinygl.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+display-test.o: ../../drivers/display.c ../../drivers/display.h ../../drivers/ledmat.h ../../drivers/test/system.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+ledmat-test.o: ../../drivers/ledmat.c ../../drivers/ledmat.h ../../drivers/test/avrtest.h ../../drivers/test/pio.h ../../drivers/test/system.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+mgetkey-test.o: ../../drivers/test/mgetkey.c ../../drivers/test/mgetkey.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+pio-test.o: ../../drivers/test/pio.c ../../drivers/test/avrtest.h ../../drivers/test/pio.h ../../drivers/test/system.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+system-test.o: ../../drivers/test/system.c ../../drivers/test/avrtest.h ../../drivers/test/mgetkey.h ../../drivers/test/pio.h ../../drivers/test/system.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+timer-test.o: ../../drivers/test/timer.c ../../drivers/test/system.h ../../drivers/test/timer.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+font-test.o: ../../utils/font.c ../../drivers/test/system.h ../../utils/font.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+pacer-test.o: ../../utils/pacer.c ../../drivers/test/system.h ../../drivers/test/timer.h ../../utils/pacer.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+tinygl-test.o: ../../utils/tinygl.c ../../drivers/display.h ../../drivers/test/system.h ../../utils/font.h ../../utils/tinygl.h
+	$(CC) -c $(CFLAGS) $< -o $@
+
+
+
+
+# Link: create executable file from object files.
+stars3: stars3-test.o display-test.o ledmat-test.o mgetkey-test.o pio-test.o system-test.o timer-test.o font-test.o pacer-test.o tinygl-test.o
+	$(CC) $(CFLAGS) $^ -o $@ -lrt
+
+
+# Clean: delete derived files.
+.PHONY: clean
+clean: 
+	-$(DEL) stars3 stars3-test.o display-test.o ledmat-test.o mgetkey-test.o pio-test.o system-test.o timer-test.o font-test.o pacer-test.o tinygl-test.o
+
+
+
diff --git a/apps/stars3/doc/Makefile b/apps/stars3/doc/Makefile
new file mode 100644
index 0000000..c93d18c
--- /dev/null
+++ b/apps/stars3/doc/Makefile
@@ -0,0 +1,45 @@
+# File:   Makefile
+# Author: M. P. Hayes, UCECE
+# Date:   11 Sep 2010
+# Descr:  Makefile for led5 docs
+
+# The scripts used to make the graphs require the program dot; this
+# is part of the graphviz package.
+
+DEL = rm
+
+all: file_dependencies.pdf module_dependencies.pdf makefile_dependencies.pdf build_dependencies.pdf callgraph.pdf
+
+file_dependencies.pdf: files.d 
+	../../../etc/graphdeps.py $< --out $@
+
+module_dependencies.pdf: modules.d 
+	../../../etc/graphdeps.py $< --modules --rotate --out $@
+
+makefile_dependencies.pdf: ../Makefile
+	../../../etc/graphdeps.py $< --out $@
+
+build_dependencies.pdf: ../Makefile
+	../../../etc/graphdeps.py $< --out $@ --showops
+
+callgraph.pdf: callgraph.d
+	../../../etc/graphdeps.py --calls --modules $< --out $@ --showops
+
+
+files.d: ../Makefile
+	(cd ..;	../../etc/makemake.py --relpath --files . . ../../drivers ../../drivers/avr ../../utils ../../extra --exclude system.h > doc/files.d)
+
+
+modules.d: ../Makefile
+	(cd ..;	../../etc/makemake.py --relpath --modules . . ../../drivers ../../drivers/avr ../../utils ../../extra --exclude system > doc/modules.d)
+
+
+callgraph.d: ../Makefile
+	(cd ..;	../../etc/makemake.py --cc="avr-gcc" --cflags="-Os -mmcu=atmega32u2" --relpath --calls . . ../../drivers ../../drivers/avr ../../utils ../../extra --exclude system.h > doc/callgraph.d)
+
+
+# Clean: delete derived files.
+.PHONY: clean
+clean: 
+	-$(DEL) *.d *.pdf
+
diff --git a/apps/stars3/doc/README b/apps/stars3/doc/README
new file mode 100644
index 0000000..39a9712
--- /dev/null
+++ b/apps/stars3/doc/README
@@ -0,0 +1,16 @@
+Running make in this directory will generate a number of PDF graphs.
+In the callgraph, the arrows means "calls".  In the dependency graphs,
+the arrows means "requires" (or "depends upon").
+
+callgraph.pdf             This shows the callgraph, i.e., what functions each
+                          function in the program calls.
+module_dependencies.pdf   This shows the dependencies between the modules.
+file_dependencies.pdf     This shows the dependencies between the files.
+makefile_dependencies.pdf This shows the dependencies required by make when
+                          building the program.
+build_dependencies.pdf    This is like makefile_dependencies.pdf but shows
+                          the operations performed to generate the new file.
+
+callgraph.d               This shows the callgraph in text format.
+files.d                   This shows the file dependencies in text format.
+modules.d                 This shows the module dependencies in text format.
diff --git a/apps/stars3/stars3.c b/apps/stars3/stars3.c
new file mode 100644
index 0000000..82ddc4a
--- /dev/null
+++ b/apps/stars3/stars3.c
@@ -0,0 +1,161 @@
+/** @file   stars1.c
+    @author M.P. Hayes
+    @date   25 Sep 2013
+    @brief  Example of using pseudorandom numbers and controlling pixel
+    brightness with PWM.  Note, pseudorandom numbers follow the same
+    sequence.
+*/
+
+#include <stdlib.h>
+#include "system.h"
+#include "pacer.h"
+#include "tinygl.h"
+
+/* This controls the range of luminance.  A bigger number gives more dynamic range
+   but requires a faster update rate.  */
+#define LUMINANCE_STEPS 25
+
+/* This needs to be fast enough to prevent the eye noticing flicker.
+   A lower value (say 5) is useful for flashing pixels.  */
+#define PWM_RATE 40
+
+/* Number of twinkling stars.  */
+#define NUM_STARS 10
+
+/* This is the rate (Hz) of luminance changes.  */
+#define TWINKLE_RATE 5
+
+#define UPDATE_RATE (LUMINANCE_STEPS * PWM_RATE)
+
+#define LOOP_RATE (TINYGL_WIDTH * UPDATE_RATE)
+
+
+static void star_twinkle (uint8_t starmap[TINYGL_HEIGHT][TINYGL_WIDTH],
+                          uint8_t x, uint8_t y, int num_levels)
+{
+    /* Check if star alive.  */
+    if (starmap[y][x] == 0)
+        return;
+
+    /* Change star luminance until it dies.  */
+    starmap[y][x]--;
+    if (starmap[y][x] > 0)
+        return;
+
+    /* Create a new star at a point neighbouring the old one
+       or at the same place.  */
+    while (1)
+    {
+        int8_t dx;
+        int8_t dy;
+        
+        dx = (rand () % 3) - 1;
+        dy = (rand () % 3) - 1;
+        
+        if (x + dx >= 0 && x + dx < TINYGL_WIDTH
+            && y + dy >= 0 && y + dy < TINYGL_HEIGHT
+            && starmap[y + dy][x + dx] == 0)
+        {
+            starmap[y + dy][x + dx] = num_levels - 1;
+            return;
+        }
+    }
+}
+
+
+static void stars_twinkle (uint8_t starmap[TINYGL_HEIGHT][TINYGL_WIDTH],
+                           int num_levels)
+{
+    uint8_t x;
+    uint8_t y;
+
+    for (x = 0; x < TINYGL_WIDTH; x++)
+    {
+        for (y = 0; y < TINYGL_HEIGHT; y++)
+        {
+            star_twinkle (starmap, x, y, num_levels);
+        }
+    }
+}
+
+
+static void stars_create (uint8_t starmap[TINYGL_HEIGHT][TINYGL_WIDTH],
+                          int num_levels)
+{
+    uint8_t x;
+    uint8_t y;
+    uint8_t i;
+
+    for (i = 0; i < NUM_STARS; i++)
+    {
+        /* Create new star, but not over a live one.  */
+        do
+        {
+            x = rand () % TINYGL_WIDTH;
+            y = rand () % TINYGL_HEIGHT;
+        } while (starmap[y][x]);
+        
+        starmap[y][x] = rand () % num_levels;
+    }
+}
+
+
+int main (void)
+{
+    uint16_t twinkle_tick = 0;
+    uint8_t pwm_tick = 0;
+    uint8_t x;
+    uint8_t y;
+    uint8_t col;
+    /* This stores the current luminance level for each pixel.  */
+    uint8_t starmap[TINYGL_HEIGHT][TINYGL_WIDTH] = {{0, }};
+    /* This controls the luminance levels.  The maximum value
+       of LUMINANCE_STEPS gives 100 percent duty cycle.   */
+    const uint8_t levels[] = {0, 1, 2, 4, 8, 15, 25, 15, 8, 4, 2, 1};
+
+    system_init ();
+
+    tinygl_init (LOOP_RATE);
+
+    pacer_init (LOOP_RATE);
+
+    stars_create (starmap, ARRAY_SIZE (levels));
+
+    while (1)
+    {
+        /* Refresh starmap.  */
+        for (col = 0; col < TINYGL_WIDTH; col++)
+        {
+            pacer_wait ();
+
+            tinygl_update ();
+        }
+
+        twinkle_tick++;
+        if (twinkle_tick >= UPDATE_RATE / TWINKLE_RATE)
+        {
+            twinkle_tick = 0;
+
+            /* Change luminance of stars until they die.  Then create
+               a new one nearby.  */
+            stars_twinkle (starmap, ARRAY_SIZE (levels));
+        }
+
+        /* Pulse width modulate pixels to control luminance.  */
+        for (x = 0; x < TINYGL_WIDTH; x++)
+        {
+            for (y = 0; y < TINYGL_HEIGHT; y++)
+            {
+                tinygl_draw_point (tinygl_point (x, y), 
+                                   levels[starmap[y][x]] > pwm_tick);
+            }
+        }
+
+        pwm_tick++;
+        if (pwm_tick >= UPDATE_RATE / PWM_RATE)
+        {
+            pwm_tick = 0;
+        }
+    }
+    return 0;
+}