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  • Get started as quickly as possible
  • Use the turtle module namespace
  • Use turtle graphics in a script
  • Use object-oriented turtle graphics
  • Turtle graphics reference
    • Turtle methods
    • Methods of TurtleScreen/Screen
    • Methods of RawTurtle/Turtle and corresponding functions
      • Turtle motion
      • Tell Turtle’s state
      • Settings for measurement
      • Pen control
        • Drawing state
        • Color control
        • Filling
        • More drawing control
        • Turtle state
          • Visibility
          • Appearance
          • Using events
          • Special Turtle methods
          • Compound shapes
          • Methods of TurtleScreen/Screen and corresponding functions
            • Window control
            • Animation control
            • Using screen events
            • Input methods
            • Settings and special methods
            • Methods specific to Screen, not inherited from TurtleScreen
            • Public classes
            • Explanation
            • Help and configuration
              • How to use help
              • Translation of docstrings into different languages
              • How to configure Screen and Turtles
              • turtledemo — Demo scripts
              • Changes since Python 2.6
              • Changes since Python 3.0
              • Introduction

                Turtle graphics is an implementation of the popular geometric drawing tools introduced in Logo , developed by Wally Feurzeig, Seymour Papert and Cynthia Solomon in 1967.

                Get started

                Imagine a robotic turtle starting at (0, 0) in the x-y plane. After an import turtle , give it the command turtle.forward(15) , and it moves (on-screen!) 15 pixels in the direction it is facing, drawing a line as it moves. Give it the command turtle.right(25) , and it rotates in-place 25 degrees clockwise.

                Turtle can draw intricate shapes using programs that repeat simple moves.

                In Python, turtle graphics provides a representation of a physical “turtle” (a little robot with a pen) that draws on a sheet of paper on the floor.

                It’s an effective and well-proven way for learners to encounter programming concepts and interaction with software, as it provides instant, visible feedback. It also provides convenient access to graphical output in general.

                Turtle drawing was originally created as an educational tool, to be used by teachers in the classroom. For the programmer who needs to produce some graphical output it can be a way to do that without the overhead of introducing more complex or external libraries into their work.

                Tutorial

                New users should start here. In this tutorial we’ll explore some of the basics of turtle drawing.

                Starting a turtle environment

                In a Python shell, import all the objects of the turtle module:

                from turtle import *
                

                If you run into a No module named '_tkinter' error, you’ll have to install the Tk interface package on your system.

                Basic drawing

                Send the turtle forward 100 steps:

                forward(100)
                

                You should see (most likely, in a new window on your display) a line drawn by the turtle, heading East. Change the direction of the turtle, so that it turns 120 degrees left (anti-clockwise):

                left(120)
                

                Let’s continue by drawing a triangle:

                forward(100)
                left(120)
                forward(100)
                

                Notice how the turtle, represented by an arrow, points in different directions as you steer it.

                Experiment with those commands, and also with backward() and right().

                Pen control

                Try changing the color - for example, color('blue') - and width of the line - for example, width(3) - and then drawing again.

                You can also move the turtle around without drawing, by lifting up the pen: up() before moving. To start drawing again, use down().

                The turtle’s position

                Send your turtle back to its starting-point (useful if it has disappeared off-screen):

                home()
                

                The home position is at the center of the turtle’s screen. If you ever need to know them, get the turtle’s x-y coordinates with:

                pos()
                

                Home is at (0, 0).

                And after a while, it will probably help to clear the window so we can start anew:

                clearscreen()
                

                Making algorithmic patterns

                Using loops, it’s possible to build up geometric patterns:

                for steps in range(100):
                    for c in ('blue', 'red', 'green'):
                        color(c)
                        forward(steps)
                        right(30)
                

                - which of course, are limited only by the imagination!

                Let’s draw the star shape at the top of this page. We want red lines, filled in with yellow:

                color('red')
                fillcolor('yellow')
                

                Just as up() and down() determine whether lines will be drawn, filling can be turned on and off:

                begin_fill()
                

                Next we’ll create a loop:

                while True:
                    forward(200)
                    left(170)
                    if abs(pos()) < 1:
                        break
                

                abs(pos()) < 1 is a good way to know when the turtle is back at its home position.

                Finally, complete the filling:

                end_fill()
                

                (Note that filling only actually takes place when you give the end_fill() command.)

                How to…

                This section covers some typical turtle use-cases and approaches.

                Get started as quickly as possible

                One of the joys of turtle graphics is the immediate, visual feedback that’s available from simple commands - it’s an excellent way to introduce children to programming ideas, with a minimum of overhead (not just children, of course).

                The turtle module makes this possible by exposing all its basic functionality as functions, available with from turtle import *. The turtle graphics tutorial covers this approach.

                It’s worth noting that many of the turtle commands also have even more terse equivalents, such as fd() for forward(). These are especially useful when working with learners for whom typing is not a skill.

                You’ll need to have the Tk interface package installed on your system for turtle graphics to work. Be warned that this is not always straightforward, so check this in advance if you’re planning to use turtle graphics with a learner.

                Use the turtle module namespace

                Using from turtle import * is convenient - but be warned that it imports a rather large collection of objects, and if you’re doing anything but turtle graphics you run the risk of a name conflict (this becomes even more an issue if you’re using turtle graphics in a script where other modules might be imported).

                The solution is to use import turtle - fd() becomes turtle.fd(), width() becomes turtle.width() and so on. (If typing “turtle” over and over again becomes tedious, use for example import turtle as t instead.)

                Use turtle graphics in a script

                It’s recommended to use the turtle module namespace as described immediately above, for example:

                import turtle as t
                from random import random
                for i in range(100):
                    steps = int(random() * 100)
                    angle = int(random() * 360)
                    t.right(angle)
                    t.fd(steps)
                

                Another step is also required though - as soon as the script ends, Python will also close the turtle’s window. Add:

                t.mainloop()
                

                to the end of the script. The script will now wait to be dismissed and will not exit until it is terminated, for example by closing the turtle graphics window.

                Use object-oriented turtle graphics

                See also

                Explanation of the object-oriented interface

                Other than for very basic introductory purposes, or for trying things out as quickly as possible, it’s more usual and much more powerful to use the object-oriented approach to turtle graphics. For example, this allows multiple turtles on screen at once.

                In this approach, the various turtle commands are methods of objects (mostly of Turtle objects). You can use the object-oriented approach in the shell, but it would be more typical in a Python script.

                The example above then becomes:

                from turtle import Turtle
                from random import random
                t = Turtle()
                for i in range(100):
                    steps = int(random() * 100)
                    angle = int(random() * 360)
                    t.right(angle)
                    t.fd(steps)
                t.screen.mainloop()
                

                Note the last line. t.screen is an instance of the Screen that a Turtle instance exists on; it’s created automatically along with the turtle.

                The turtle’s screen can be customised, for example:

                t.screen.title('Object-oriented turtle demo')
                t.screen.bgcolor("orange")
                

                In the following documentation the argument list for functions is given. Methods, of course, have the additional first argument self which is omitted here.

                Turtle methods

                Turtle motion
                Move and draw
                Tell Turtle’s state
                Setting and measurement

                Methods of RawTurtle/Turtle and corresponding functions

                Most of the examples in this section refer to a Turtle instance called turtle.

                Turtle motion

                turtle.forward(distance) turtle.fd(distance)
                Parameters:

                distance – a number (integer or float)

                Move the turtle forward by the specified distance, in the direction the turtle is headed.

                >>> turtle.position()
                (0.00,0.00)
                >>> turtle.forward(25)
                >>> turtle.position()
                (25.00,0.00)
                >>> turtle.forward(-75)
                >>> turtle.position()
                (-50.00,0.00)
                

                Move the turtle backward by distance, opposite to the direction the turtle is headed. Do not change the turtle’s heading.

                >>> turtle.position()
                (0.00,0.00)
                >>> turtle.backward(30)
                >>> turtle.position()
                (-30.00,0.00)
                

                Turn turtle right by angle units. (Units are by default degrees, but can be set via the degrees() and radians() functions.) Angle orientation depends on the turtle mode, see mode().

                >>> turtle.heading()
                >>> turtle.right(45)
                >>> turtle.heading()
                337.0
                

                Turn turtle left by angle units. (Units are by default degrees, but can be set via the degrees() and radians() functions.) Angle orientation depends on the turtle mode, see mode().

                >>> turtle.heading()
                >>> turtle.left(45)
                >>> turtle.heading()
                

                If y is None, x must be a pair of coordinates or a Vec2D (e.g. as returned by pos()).

                Move turtle to an absolute position. If the pen is down, draw line. Do not change the turtle’s orientation.

                >>> tp = turtle.pos()
                (0.00,0.00)
                >>> turtle.setpos(60,30)
                >>> turtle.pos()
                (60.00,30.00)
                >>> turtle.setpos((20,80))
                >>> turtle.pos()
                (20.00,80.00)
                >>> turtle.setpos(tp)
                >>> turtle.pos()
                (0.00,0.00)
                

                Move turtle to an absolute position. Unlike goto(x, y), a line will not be drawn. The turtle’s orientation does not change. If currently filling, the polygon(s) teleported from will be filled after leaving, and filling will begin again after teleporting. This can be disabled with fill_gap=True, which makes the imaginary line traveled during teleporting act as a fill barrier like in goto(x, y).

                >>> tp = turtle.pos()
                (0.00,0.00)
                >>> turtle.teleport(60)
                >>> turtle.pos()
                (60.00,0.00)
                >>> turtle.teleport(y=10)
                >>> turtle.pos()
                (60.00,10.00)
                >>> turtle.teleport(20, 30)
                >>> turtle.pos()
                (20.00,30.00)
                

                Added in version 3.12.

                Set the turtle’s first coordinate to x, leave second coordinate unchanged.

                >>> turtle.position()
                (0.00,240.00)
                >>> turtle.setx(10)
                >>> turtle.position()
                (10.00,240.00)
                

                Set the turtle’s second coordinate to y, leave first coordinate unchanged.

                >>> turtle.position()
                (0.00,40.00)
                >>> turtle.sety(-10)
                >>> turtle.position()
                (0.00,-10.00)
                

                Set the orientation of the turtle to to_angle. Here are some common directions in degrees:

                standard mode

                logo mode

                0 - east

                0 - north

                90 - north

                90 - east

                180 - west

                180 - south

                270 - south

                270 - west

                >>> turtle.setheading(90)
                >>> turtle.heading()
                turtle.home()
                

                Move turtle to the origin – coordinates (0,0) – and set its heading to its start-orientation (which depends on the mode, see mode()).

                >>> turtle.heading()
                >>> turtle.position()
                (0.00,-10.00)
                >>> turtle.home()
                >>> turtle.position()
                (0.00,0.00)
                >>> turtle.heading()
                

                Draw a circle with given radius. The center is radius units left of the turtle; extent – an angle – determines which part of the circle is drawn. If extent is not given, draw the entire circle. If extent is not a full circle, one endpoint of the arc is the current pen position. Draw the arc in counterclockwise direction if radius is positive, otherwise in clockwise direction. Finally the direction of the turtle is changed by the amount of extent.

                As the circle is approximated by an inscribed regular polygon, steps determines the number of steps to use. If not given, it will be calculated automatically. May be used to draw regular polygons.

                >>> turtle.home()
                >>> turtle.position()
                (0.00,0.00)
                >>> turtle.heading()
                >>> turtle.circle(50)
                >>> turtle.position()
                (-0.00,0.00)
                >>> turtle.heading()
                >>> turtle.circle(120, 180)  # draw a semicircle
                >>> turtle.position()
                (0.00,240.00)
                >>> turtle.heading()
                180.0
                

                Draw a circular dot with diameter size, using color. If size is not given, the maximum of pensize+4 and 2*pensize is used.

                >>> turtle.home()
                >>> turtle.dot()
                >>> turtle.fd(50); turtle.dot(20, "blue"); turtle.fd(50)
                >>> turtle.position()
                (100.00,-0.00)
                >>> turtle.heading()
                turtle.stamp()
                

                Stamp a copy of the turtle shape onto the canvas at the current turtle position. Return a stamp_id for that stamp, which can be used to delete it by calling clearstamp(stamp_id).

                >>> turtle.color("blue")
                >>> stamp_id = turtle.stamp()
                >>> turtle.fd(50)
                

                Delete all or first/last n of turtle’s stamps. If n is None, delete all stamps, if n > 0 delete first n stamps, else if n < 0 delete last n stamps.

                >>> for i in range(8):
                ...     unused_stamp_id = turtle.stamp()
                ...     turtle.fd(30)
                >>> turtle.clearstamps(2)
                >>> turtle.clearstamps(-2)
                >>> turtle.clearstamps()
                turtle.undo()
                

                Undo (repeatedly) the last turtle action(s). Number of available undo actions is determined by the size of the undobuffer.

                >>> for i in range(4):
                ...     turtle.fd(50); turtle.lt(80)
                >>> for i in range(8):
                ...     turtle.undo()
                

                Set the turtle’s speed to an integer value in the range 0..10. If no argument is given, return current speed.

                If input is a number greater than 10 or smaller than 0.5, speed is set to 0. Speedstrings are mapped to speedvalues as follows:

              • “fastest”: 0

              • “fast”: 10

              • “normal”: 6

              • “slow”: 3

              • “slowest”: 1

              • Speeds from 1 to 10 enforce increasingly faster animation of line drawing and turtle turning.

                Attention: speed = 0 means that no animation takes place. forward/back makes turtle jump and likewise left/right make the turtle turn instantly.

                >>> turtle.speed()
                >>> turtle.speed('normal')
                >>> turtle.speed()
                >>> turtle.speed(9)
                >>> turtle.speed()
                turtle.pos()
                

                Return the turtle’s current location (x,y) (as a Vec2D vector).

                >>> turtle.pos()
                (440.00,-0.00)
                

                Return the angle between the line from turtle position to position specified by (x,y), the vector or the other turtle. This depends on the turtle’s start orientation which depends on the mode - “standard”/”world” or “logo”.

                >>> turtle.goto(10, 10)
                >>> turtle.towards(0,0)
                225.0
                turtle.heading()
                

                Return the turtle’s current heading (value depends on the turtle mode, see mode()).

                >>> turtle.home()
                >>> turtle.left(67)
                >>> turtle.heading()
                

                Return the distance from the turtle to (x,y), the given vector, or the given other turtle, in turtle step units.

                >>> turtle.home()
                >>> turtle.distance(30,40)
                >>> turtle.distance((30,40))
                >>> joe = Turtle()
                >>> joe.forward(77)
                >>> turtle.distance(joe)
                

                Set angle measurement units, i.e. set number of “degrees” for a full circle. Default value is 360 degrees.

                >>> turtle.home()
                >>> turtle.left(90)
                >>> turtle.heading()
                >>> # Change angle measurement unit to grad (also known as gon,
                >>> # grade, or gradian and equals 1/100-th of the right angle.)
                >>> turtle.degrees(400.0)
                >>> turtle.heading()
                100.0
                >>> turtle.degrees(360)
                >>> turtle.heading()
                turtle.radians()
                

                Set the angle measurement units to radians. Equivalent to degrees(2*math.pi).

                >>> turtle.home()
                >>> turtle.left(90)
                >>> turtle.heading()
                >>> turtle.radians()
                >>> turtle.heading()
                1.5707963267948966
                

                Set the line thickness to width or return it. If resizemode is set to “auto” and turtleshape is a polygon, that polygon is drawn with the same line thickness. If no argument is given, the current pensize is returned.

                >>> turtle.pensize()
                >>> turtle.pensize(10)   # from here on lines of width 10 are drawn
                

                Return or set the pen’s attributes in a “pen-dictionary” with the following key/value pairs:

              • “shown”: True/False

              • “pendown”: True/False

              • “pencolor”: color-string or color-tuple

              • “fillcolor”: color-string or color-tuple

              • “pensize”: positive number

              • “speed”: number in range 0..10

              • “resizemode”: “auto” or “user” or “noresize”

              • “stretchfactor”: (positive number, positive number)

              • “outline”: positive number

              • “tilt”: number

              • This dictionary can be used as argument for a subsequent call to pen() to restore the former pen-state. Moreover one or more of these attributes can be provided as keyword-arguments. This can be used to set several pen attributes in one statement.

                >>> turtle.pen(fillcolor="black", pencolor="red", pensize=10)
                >>> sorted(turtle.pen().items())
                [('fillcolor', 'black'), ('outline', 1), ('pencolor', 'red'),
                 ('pendown', True), ('pensize', 10), ('resizemode', 'noresize'),
                 ('shearfactor', 0.0), ('shown', True), ('speed', 9),
                 ('stretchfactor', (1.0, 1.0)), ('tilt', 0.0)]
                >>> penstate=turtle.pen()
                >>> turtle.color("yellow", "")
                >>> turtle.penup()
                >>> sorted(turtle.pen().items())[:3]
                [('fillcolor', ''), ('outline', 1), ('pencolor', 'yellow')]
                >>> turtle.pen(penstate, fillcolor="green")
                >>> sorted(turtle.pen().items())[:3]
                [('fillcolor', 'green'), ('outline', 1), ('pencolor', 'red')]
                

                Four input formats are allowed:

                pencolor()

                Return the current pencolor as color specification string or as a tuple (see example). May be used as input to another color/pencolor/fillcolor call.

                pencolor(colorstring)

                Set pencolor to colorstring, which is a Tk color specification string, such as "red", "yellow", or "#33cc8c".

                pencolor((r, g, b))

                Set pencolor to the RGB color represented by the tuple of r, g, and b. Each of r, g, and b must be in the range 0..colormode, where colormode is either 1.0 or 255 (see colormode()).

                pencolor(r, g, b)

                Set pencolor to the RGB color represented by r, g, and b. Each of r, g, and b must be in the range 0..colormode.

                If turtleshape is a polygon, the outline of that polygon is drawn with the newly set pencolor.

                >>> colormode()
                >>> turtle.pencolor()
                'red'
                >>> turtle.pencolor("brown")
                >>> turtle.pencolor()
                'brown'
                >>> tup = (0.2, 0.8, 0.55)
                >>> turtle.pencolor(tup)
                >>> turtle.pencolor()
                (0.2, 0.8, 0.5490196078431373)
                >>> colormode(255)
                >>> turtle.pencolor()
                (51.0, 204.0, 140.0)
                >>> turtle.pencolor('#32c18f')
                >>> turtle.pencolor()
                (50.0, 193.0, 143.0)
                turtle.fillcolor(*args)
                

                Return or set the fillcolor.

                Four input formats are allowed:

                fillcolor()

                Return the current fillcolor as color specification string, possibly in tuple format (see example). May be used as input to another color/pencolor/fillcolor call.

                fillcolor(colorstring)

                Set fillcolor to colorstring, which is a Tk color specification string, such as "red", "yellow", or "#33cc8c".

                fillcolor((r, g, b))

                Set fillcolor to the RGB color represented by the tuple of r, g, and b. Each of r, g, and b must be in the range 0..colormode, where colormode is either 1.0 or 255 (see colormode()).

                fillcolor(r, g, b)

                Set fillcolor to the RGB color represented by r, g, and b. Each of r, g, and b must be in the range 0..colormode.

                If turtleshape is a polygon, the interior of that polygon is drawn with the newly set fillcolor.

                >>> turtle.fillcolor("violet")
                >>> turtle.fillcolor()
                'violet'
                >>> turtle.pencolor()
                (50.0, 193.0, 143.0)
                >>> turtle.fillcolor((50, 193, 143))  # Integers, not floats
                >>> turtle.fillcolor()
                (50.0, 193.0, 143.0)
                >>> turtle.fillcolor('#ffffff')
                
                
                
                
                    
                
                >>> turtle.fillcolor()
                (255.0, 255.0, 255.0)
                turtle.color(*args)
                

                Return or set pencolor and fillcolor.

                Several input formats are allowed. They use 0 to 3 arguments as follows:

                color()

                Return the current pencolor and the current fillcolor as a pair of color specification strings or tuples as returned by pencolor() and fillcolor().

                color(colorstring), color((r,g,b)), color(r,g,b)

                Inputs as in pencolor(), set both, fillcolor and pencolor, to the given value.

                color(colorstring1, colorstring2), color((r1,g1,b1), (r2,g2,b2))

                Equivalent to pencolor(colorstring1) and fillcolor(colorstring2) and analogously if the other input format is used.

                If turtleshape is a polygon, outline and interior of that polygon is drawn with the newly set colors.

                >>> turtle.color("red", "green")
                >>> turtle.color()
                ('red', 'green')
                >>> color("#285078", "#a0c8f0")
                >>> color()
                ((40.0, 80.0, 120.0), (160.0, 200.0, 240.0))
                turtle.filling()
                

                Return fillstate (True if filling, False else).

                >>> turtle.begin_fill()
                >>> if turtle.filling():
                ...    turtle.pensize(5)
                ... else:
                ...    turtle.pensize(3)
                turtle.end_fill()
                

                Fill the shape drawn after the last call to begin_fill().

                Whether or not overlap regions for self-intersecting polygons or multiple shapes are filled depends on the operating system graphics, type of overlap, and number of overlaps. For example, the Turtle star above may be either all yellow or have some white regions.

                >>> turtle.color("black", "red")
                >>> turtle.begin_fill()
                >>> turtle.circle(80)
                >>> turtle.end_fill()
                turtle.reset()
                

                Delete the turtle’s drawings from the screen, re-center the turtle and set variables to the default values.

                >>> turtle.goto(0,-22)
                >>> turtle.left(100)
                >>> turtle.position()
                (0.00,-22.00)
                >>> turtle.heading()
                100.0
                >>> turtle.reset()
                >>> turtle.position()
                (0.00,0.00)
                >>> turtle.heading()
                turtle.clear()
                

                Delete the turtle’s drawings from the screen. Do not move turtle. State and position of the turtle as well as drawings of other turtles are not affected.

                turtle.write(arg, move=False, align='left', font=('Arial', 8, 'normal'))
                Parameters:
              • arg – object to be written to the TurtleScreen

              • move – True/False

              • align – one of the strings “left”, “center” or right”

              • font – a triple (fontname, fontsize, fonttype)

              • Write text - the string representation of arg - at the current turtle position according to align (“left”, “center” or “right”) and with the given font. If move is true, the pen is moved to the bottom-right corner of the text. By default, move is False.

                >>> turtle.write("Home = ", True, align="center")
                >>> turtle.write((0,0), True)
                turtle.ht()
                

                Make the turtle invisible. It’s a good idea to do this while you’re in the middle of doing some complex drawing, because hiding the turtle speeds up the drawing observably.

                >>> turtle.hideturtle()
                turtle.isvisible()
                

                Return True if the Turtle is shown, False if it’s hidden.

                >>> turtle.hideturtle()
                >>> turtle.isvisible()
                False
                >>> turtle.showturtle()
                >>> turtle.isvisible()
                

                Set turtle shape to shape with given name or, if name is not given, return name of current shape. Shape with name must exist in the TurtleScreen’s shape dictionary. Initially there are the following polygon shapes: “arrow”, “turtle”, “circle”, “square”, “triangle”, “classic”. To learn about how to deal with shapes see Screen method register_shape().

                >>> turtle.shape()
                'classic'
                >>> turtle.shape("turtle")
                >>> turtle.shape()
                'turtle'
                

                Set resizemode to one of the values: “auto”, “user”, “noresize”. If rmode is not given, return current resizemode. Different resizemodes have the following effects:

              • “auto”: adapts the appearance of the turtle corresponding to the value of pensize.

              • “user”: adapts the appearance of the turtle according to the values of stretchfactor and outlinewidth (outline), which are set by shapesize().

              • “noresize”: no adaption of the turtle’s appearance takes place.

              • resizemode("user") is called by shapesize() when used with arguments.

                >>> turtle.resizemode()
                'noresize'
                >>> turtle.resizemode("auto")
                >>> turtle.resizemode()
                'auto'
                turtle.shapesize(stretch_wid=None, stretch_len=None, outline=None)
                turtle.turtlesize(stretch_wid=None, stretch_len=None, outline=None)
                
                Parameters:
              • stretch_wid – positive number

              • stretch_len – positive number

              • outline – positive number

              • Return or set the pen’s attributes x/y-stretchfactors and/or outline. Set resizemode to “user”. If and only if resizemode is set to “user”, the turtle will be displayed stretched according to its stretchfactors: stretch_wid is stretchfactor perpendicular to its orientation, stretch_len is stretchfactor in direction of its orientation, outline determines the width of the shape’s outline.

                >>> turtle.shapesize()
                (1.0, 1.0, 1)
                >>> turtle.resizemode("user")
                >>> turtle.shapesize(5, 5, 12)
                >>> turtle.shapesize()
                (5, 5, 12)
                >>> turtle.shapesize(outline=8)
                >>> turtle.shapesize()
                (5, 5, 8)
                

                Set or return the current shearfactor. Shear the turtleshape according to the given shearfactor shear, which is the tangent of the shear angle. Do not change the turtle’s heading (direction of movement). If shear is not given: return the current shearfactor, i. e. the tangent of the shear angle, by which lines parallel to the heading of the turtle are sheared.

                >>> turtle.shape("circle")
                >>> turtle.shapesize(5,2)
                >>> turtle.shearfactor(0.5)
                >>> turtle.shearfactor()
                

                Rotate the turtleshape by angle from its current tilt-angle, but do not change the turtle’s heading (direction of movement).

                >>> turtle.reset()
                >>> turtle.shape("circle")
                >>> turtle.shapesize(5,2)
                >>> turtle.tilt(30)
                >>> turtle.fd(50)
                >>> turtle.tilt(30)
                >>> turtle.fd(50)
                

                Set or return the current tilt-angle. If angle is given, rotate the turtleshape to point in the direction specified by angle, regardless of its current tilt-angle. Do not change the turtle’s heading (direction of movement). If angle is not given: return the current tilt-angle, i. e. the angle between the orientation of the turtleshape and the heading of the turtle (its direction of movement).

                >>> turtle.reset()
                >>> turtle.shape("circle")
                >>> turtle.shapesize(5,2)
                >>> turtle.tilt(45)
                >>> turtle.tiltangle()
                turtle.shapetransform(t11=None, t12=None, t21=None, t22=None)
                
                Parameters:
              • t11 – a number (optional)

              • t12 – a number (optional)

              • t21 – a number (optional)

              • t12 – a number (optional)

              • Set or return the current transformation matrix of the turtle shape.

                If none of the matrix elements are given, return the transformation matrix as a tuple of 4 elements. Otherwise set the given elements and transform the turtleshape according to the matrix consisting of first row t11, t12 and second row t21, t22. The determinant t11 * t22 - t12 * t21 must not be zero, otherwise an error is raised. Modify stretchfactor, shearfactor and tiltangle according to the given matrix.

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