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CS111 Computer Programming
Department of Computer Science Wellesley College
Spirals, Trees, and Snowflakes
TurtleWorld
Tuesday, October 17, 2006 TurtleWorld 11- 2
Honey, I shrunk the Buggle
o Turtles* are like Buggles,
only smaller** and more
carefree (no grid).
o To create a new Turtle
new Turtle();
o At birth, Turtles are
centered, pointing EAST,
pen*** down, and red.
- If you have programmed in LOGO, Turtles should be old friends. ** So small, in fact, that you cannot see them. *** Turtles have pens rather than brushes.
TurtleWorld 11- 3 Turtle Commands Go Forward: public void fd (double dist); Go Backward: public void bd (double dist); Turn Left: public void lt (double angle); Turn Right: public void rt (double angle); Pen Up: public void pu(); Pen Down: public void pd(); Get Heading: public double getHeading(); Set Heading: public void setHeading (double newHeading); Get Color: public Color getColor(); Set Color: public void setColor (Color newColor); Get Position: public double getX(); public double getY(); Set Position: public setX(double newX); public setY(double newY); public setPosition(double newX, double newY); Go Home (to point (0,0), facing east, pen down): public void home ();
- When a double parameter is specified, Java will automatically convert an int argument to a double. E.g. fd(36); is treated like fd(36.0); TurtleWorld 11- 4 What’s a double?
It’s a double-precision floating point number. E.g.:
double x = 3.72; x + 1.234 // Value = 4. x + 2 // Value = 5.72 (2 automatically converted to 2.0 first) x * 2 // Value = 7.44 (2 automatically converted to 2.0 first) x / 2 // Value = 1.86 (2 automatically converted to 2.0 first) (int) x // Value = 3 (“int cast”, converts to integer by truncation) Math.round(x) // Value = 4 (rounds to nearest integer) Math.floor(x) // Value = 3 (rounds toward negative infinity) Math.floor(-5.12) // Value = -6 (rounds toward negative infinity) Math.ceiling(x) // Value = 4 (rounds toward positive infinity) Math.ceiling(-5.12) // Value = -5 (rounds toward positive infinity) (double) 17 // Value = 17.0 (“double cast”, converts to a double)
TurtleWorld 11- 7 Spiro the Spiraling Turtle spiro.spiral(50,90,0,3); spiro.spiral(50,72,0,2); spiro.spiral(30,120,0,6); spiro.spiral(40,60,0,6); TurtleWorld 11- 8 spiral(steps, angle, length, increment); 0 fd( 0 ); lt( 90 ); length angle 3 fd(0+ 3 ); lt(90); increment 6 fd(3+3); lt(90); 9 fd(6+3); lt(90); 12 fd(9+3); lt(90); E.g., spiral(100, 90, 0, 3); 100 steps remain 99 steps remain 98 steps remain 97 steps remain 96 steps remain 95 steps remain.. . (0,0)
TurtleWorld 11- 9 After 100 Steps: TurtleWorld 11- 10 Designing a Java spiral() Method spiral(5, 90, 0, 3); steps angle length increment 0 fd(0); lt(90); spiral(4,90,3,3);^3 fd(3); lt(90); spiral(3,90,6,3); 6 fd(6); lt(90); spiral(2,90,9,3); 9 fd(9); lt(90); spiral(1,90,12,3); remains to be done 12 fd(12); lt(90); spiral(0,90,12,3);
Think invocation trees!
TurtleWorld 11- 13 trina.tree(7,75,30,0.8) trina.tree(7,75,15,0.8) TreeWorld trina.tree(10,80,45,0.7) trina.tree(10,100,90,0.68) TurtleWorld 11- 14 How to make a level 4 tree Make a trunk and two level 3 trees with 60% trunks set at 45° angles fd(100); rt(45); make level 3 tree w/ trunk 0.6 lt(245); make level 3 tree w/ trunk 0.6* rt(45); bd(100);**
TurtleWorld 11- 15 How to make a level 3 tree Make a trunk 0.6 as long as before fd(60); rt(45); make level 2 tree w/ trunk 0.6 lt(245); make level 2 tree w/ trunk 0.6* rt(45); bd(60);** and two level 2 trees with 60% trunks set at 45° angles TurtleWorld 11- 16 How to make a level 2 tree Make a trunk 0.6 as long as before and two level 1 trees With 60% trunks set at 45° angles fd(36); rt(45); make level 1 tree w/ trunk 0.6 lt(245); make level 1 tree w/ trunk 0.6* rt(45); bd(36);**
TurtleWorld 11- 19 Let’s Write tree() in Java public void tree(int levels, double length, double angle, double shrink) { } TurtleWorld 11- 20 Snowflakes (the Koch curve) snowy.snowflake(0.200); snowy.snowflake(2.200); snowy.snowflake(1.200); snowy.snowflake(3.200);
TurtleWorld 11- 21 A Snowflake has 3 Sides public void snowflake (int levels, double length) { snowside(levels, length); rt(120); snowside(levels, length); rt(120); snowside(levels, length); rt(120); } snowy.snowside(0,200); snowy.snowside(1,200); snowy.snowside(2,200); snowy.snowside(^3 ,200); TurtleWorld 11- 22 Let’s Write snowside() in Java public void snowside (int levels, double length) { }
