· Expressions

o Expressions are made up of the following:

§ Constants: Real or complex constants. Examples:

· 1+2i

· 4.3

· -6.77i

· _pi (this is currently the only built-in constant. For e, use exp(1).)

§ Variables: the letter z.

§ Unary functions: These have the form name(expression), where expression is any expression and name comes from the following:

· con: complex conjugate

· cos: complex cosine

· sin: complex sine

· tan: complex tangent (sin / cos)

· exp: e raised to the power given by expression

· arg: argument in radians

· rea: real part

· ima: imaginary part

· mod: complex modulus

· log: principle branch of the complex logarithm

§ Binary functions: These have the form name(expression1,expression2), where expression1 and expression2 are any expressions and name comes from the following:

· add: addition

· sub: subtraction

· mul: multiplication

· div: division

· pow: expression1raised the power given by expression2

o Examples of expressions:

§ add(mul(3,z),5): this represents the expression 3z + 5

§ mul(z,exp(z)): this represents the expression ze^z

§ cos(pow(z,.5)): this represents the expression cos(sqrt(z))

· The Iterate Panel

o

o The Iterate panel allows you to generate a filled Julia set for the function entered into the “w =” expression box.

o You can change the color scheme (before you graph) by clicking the “Change Colors” button.

o To begin iteration, click the “Iterate” button. Make sure that an expression is entered in blue at the bottom of the applet window.

o Iteration Parameters:

§ MaxIter: The maximum number of iterations to execute. This must be a positive integer.

§ Mod: the maximum modulus a point’s orbit can have before it is considered to have escaped. If this number is zero or negative, the modulus is not taken into consideration.

§ Re: the maximum real part a point’s orbit can have before it is considered to have escaped. By clicking on the “Re <” label, you can make the maximum an absolute value.

§ Im: the maximum imaginary part a point’s orbit can have before it is considered to have escaped. By clicking on the “Im <” label, you can make the maximum an absolute value.

· The Graph Panel

o

o The Graph panel allows you to graph any function. You simply enter the function into the Expression box, click OK, and click and/or drag on the z-panel (on the left). The result of the function will appear on the right.

· Zoom panels

o Using the zoom panel, you can adjust the window size for the graphs. When the Graph panel is shown, the z-plane and the w-plane can be adjusted separately.

· Other Options

o Draw Axes

§ When this box is checked, the real and imaginary axes will be drawn, in addition to the unit circle centered at the origin.

o Mandelbrot

§ When this box is checked, the Graph panel will not be available. The Iterate panel will generate the Mandelbrot rather than evaluating any expression.

o Draw In New Window

§ When this box is checked, the Iterate button will open a new window, with a user-defined size, rather than graphing in the regular plane.

o Keep Square

§ This option adjusts the size of the new window to keep the pixels square; this prevents distortion of the image.

o Clear

§ Clears the current panel (Iterate panel or Graph panel).