How to use "The Fractal Microscope"


  • Zooming in and out
  • Changing from the Mandelbrot set to the Julia set
  • Changing from the Julia set to the Mandelbrot set
  • Zoom in/out n times
  • Drag and Zoom
  • Show me the Julia set
  • Take me back to the Mandelbrot set
  • Coordinate Information
  • Quick Julia
  • The "Update" Bar
  • Set Corners...
  • Set Depth...
  • Julia Seed...
  • Mandelbrot Set...
  • Palette
  • Formula
  • Image Size
  • Logarithmic Smoothing
  • Investigate Orbits
  • Questions and Comments

    Zooming in and out

    There are three ways to zoom in and out with the Fractal Microscope:

  • Turn on the checkbox beside "Zoom" under "When I Click:." Select a zoom factor from the list beside the word "Zoom." Now click somewhere on the image. The image will redraw, centered at the point you clicked and zoomed in or out the number of times you specified. You do not have to press the update bar to see these changes.

  • Alternatively, you can turn on the checkbox beside "Drag and Zoom" under "When I Click:." Click on the image, but don't let the mouse button up! Drag the mouse over the region you want to zoom in on. The Fractal Microscope will only let you drag a square area. You will see a different-colored square over the area you have dragged. When you let the mouse button up, this area will fill the image.

    If you start to drag a zoom area and decide that you don't really want to zoom in, just move the mouse off the image and let the mouse button up there. Nothing will happen.

    You do not have to press update to make drag and zoom take effect.

  • You can also use the "Set Corners" button to zoom.

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    Changing from the Mandelbrot set to the Julia set

    There are two ways to change from the Mandelbrot set to the Julia set:

  • Turn on the checkbox beside "Show me the Julia set" under "When I Click:." Now click on the point in the Mandelbrot set that you want to use as the seed to draw a Julia set. The Julia set is calculated as soon as you click; you don't have to press update.

  • Or, you can click the button labelled "Julia Seed..." A dialog box will appear. Type in the x and y coordinates that you want to use for the seed and make sure the checkbox beside "Change to Julia set now" is on. Click "OK." You will have to press update to see the Julia set.

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    Changing from the Julia set to the Mandelbrot set

    There are two ways to change from the Julia set to the Mandelbrot set:

  • Turn on the checkbox beside "Take me back to the Mandelbrot set" under "When I click:." Now click on the image. The Mandelbrot set will be drawn, using the point you clicked as its center. You don't have to press update.

  • Or, you can click on the button labelled "Mandelbrot Set..." A dialog box will appear. Choose whether you want to go back to the Mandelbrot set with the same corners you had before you started investigating the Julia set or with the default corners that Fractal Microscope starts up with. Click "OK." You have to press the update bar before you see the changes.

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    Coordinate Information

    Turn this checkbox on to see the information window. This window tells you what point your mouse is at when it's over the image and how many iterations it took for that point to escape. This can be used with "Drag and Zoom" to zoom in on a particular area.

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    Quick Julia

    This checkbox shows and hides a window that draws an outline of the Julia set using a fast algorithm. This "quick" Julia set is not as detailed as the Julia sets you can generate in the main window, but it can give you an idea of what the set looks like.

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    The "Update" Bar

    If you change the corners, depth, formula, or some other setting and the image doesn't seem to change, you probably forgot to press this. Hitting the update bar causes the picture of the Mandelbrot or Julia set to be updated. For most of the controls above the update bar, no changes will take effect until you hit the update bar. This is so that you can make several changes without taking the time to recalculate after each one.

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    Set Corners...

    This displays a dialog box which lets you set the left, right, top, and bottom bounds of the image drawn. There are two ways to do this:

  • Clicking the checkbox next to "Use these corners" lets you type in the bounds directly. Note that these bounds must define a square (the difference between left and right must equal the difference between bottom and top). If they aren't square, the program will make them square for you.

  • The other way to set the corners is by specifying a center. To do this, click the checkbox next to "Use this center." Now you can type in the point you want the image to be centered on, as well as a magnification. If you just want to re-center without zooming in, enter a magnification of one.

    You have to press the update bar before changes to the corners take effect.

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    Set Depth...

    The depth determines how many times the Fractal Microscope iterates before it decides a point is in the Mandelbrot or Julia set and colors it black. Setting the depth higher gives a more defined image. It also makes the image take longer to draw. If you zoom in very close, you'll want to increase the depth to see greater detail. You must press the update bar before changes to depth take effect.

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    Logarithmic Smoothing

    Toggle this checkbx to turn logarithmic smoothing on and off. Logarithmic smoothing is an alternative color scheme that shows a greater variety of colors. You have to press update before this change takes effect.

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    Palette

    These are different color schemes for painting the Mandelbrot or Julia set. You don't have to click update after changing the palette.

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    Formula

    Select an exponent between two and ten. The standard Mandelbrot set uses two. Press the update bar after setting this to make the change take effect.

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    Image Size

    The size of the image has a big effect on the time it takes the Fractal Microscope to draw it. If you have a slow computer, you'll want to set this low (100x100). If you have a really fast computer or don't mind a wait, you can try the higher resolutions. Resolutions higher than 400x400 are available in the large version of the Fractal Microscope. Note that a size change does not take effect until you press update.

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    Investigate Orbits

    This button brings up a separate window that lets you see the path taken by the iteration of a point. This window is complex enough that it gets its own help page.

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    Questions and Comments

    If you still have questions about how to use The Fractal Microscope, or you have suggestions about how to make it better, send e-mail to Alton Patrick.

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