This is part seven of the Beginners Guide to Writing Fractal formulas.
you can do this tutorial at any time.

After a nice rest of our little gray cells we embark on a wild excursion
to Switch land.  The switch feature allows you to expand the mandel type
catalogue into individual Julia type mappings.  Or simply stated you can
search through your mandel map and see a preview of what the Julia map
looks like.  click and a Julia mapping comes up.  UF has a special section
that you can add to a formula after the default section called Switch.

I added the switch to our formula and it was way to complicated so I
figured I'd make a new fractal for the tutorial.  That way I won't loos
anyone.

In preparation:
    Start UF 
    Click the edit icon to edit the formula
    Create two new formula shells one called Ftswitch7M and one called
Ftswitch7J

So you should have:

    Ftswitch7M{
    Init:
    Loop:
    Bailout:
    Default:
    }
and
    Ftswitch7J{
    Init:
    Loop:
    Bailout:
    Default:
    }

Theses two formulas will be our switch formulas.  The switch section is an
addon to the end of the formula that looks like the following.

Switch:
  Type = "Ftswitch7J"
  Other assignments

The Type assignment is important because this tells UF what formula to
look at and load to do the switch.

Lets add a Switch section at the end of our formulas.  And make the switch
formula connections.
    Ftswitch7M{
    Init:
    Loop:
    Bailout:
    Default:
    Switch:
      Type = "Ftswitch7J
    }
and
    Ftswitch7J{
    Init:
    Loop:
    Bailout:
    Default:
    Switch:
      Type = "Ftswitch7M
    }

Now lets make up a fractal formula

Lets pick an equation to use.  (once again a hs algebra book)
    y = a*b*x/(a^2+x^2)    called a serpentine curve
Let me see if I can remember what to do...
Replace my x with a z
    y = a*b*z/(a^2+z^2)
Replace my y with a z
    z = a*b*z/(a^2+z^2)

Pretty easy, now lets put that into the loop section of the M formula
only.

Lets initialize the z to #pixel and replace the a's with #pixel.
Lets do this in our M formula.
So it looks like this:

Ftswitch7m{
init:
  z=#pixel
LOOP:
  z = #pixel*b*z/(#pixel^2+z^2)
Bailout:

Default:

Switch:
  Type = "Ftswitch7J"
}

Lets make b user selectable by adding a param block in the default
section.

Param brad
  hint = "this is the radius of the circle\
        That is tangent to the serpentine curve.
  Caption = "B Radius"
  Default = (1.0,0.0)
Endparam

Lets add above the param block into our formulas default section and put
the
definition
    B = @brad
In the init section.  Lastly lets put the bailout in.
    |z|<4
(good place to start out anyways)

The formula should look like this:
Ftswitch7m{
init:
  b= @brad
  z=#pixel
LOOP:
  z = #pixel*b*z/(#pixel^2+z^2)
Bailout:
  |z| < 4
Default:
    Param brad
      hint = "this is the radius of the circle\
                        That is tangent to the
serpentine curve."
      Caption = "B in abz/(sqr(a)+sqr(z))"
      Default = (1.0,0.0)
    endparam

Switch:
  type = "Ftswitch7J"
}

Lets save our work make sure we turn on strict type checking and load the
M formula to see if its ok.  Lets do that.
Everything should be very nice at this point.

What are we switching anyways?
Normally the constant that gets switched is the constant that is being
added or operated on by the basic iteration formula.  For clarification
the mandelbrot map after every iteration terminates has the C initialized
to the next pixel value.  The Julia map has the C value initialized to the
same start value, after every terminated iteration.

How does this apply to our formula?
In our formula 
    z = #pixel*b*z/(#pixel^2+z^2)
The #pixel value is reinitialized to the current starting pixel at every
iteration.  This is the variable that we want to Julia switch switch.

What exactly do we want that switch to do?
We want to tell uf, when we click the switch icon, is:
    What formula do I load for this switch
Whats the name of the variable to switch and what value will it have in
the switched formula?
What other variables do I need to carry over to the switched formula

So lets look at our switch section

    Ftswitch7m{
    .
    .
    .
    Switch:
      type = "Ftswitch7J"
    }

We've told it what the switch formula is already so lets tell it what the
variable name is and what value we want it to pass along.  In our case
it's the value of the pixel as the cursor moves over our image.

Ftswitch7m{
.
.
.
Switch:
  type = "Ftswitch7J"
  flop = #pixel
}

And now we need to carry over whatever variables we are currently using.

Ftswitch7m{
.
.
.
Switch:
  type = "Ftswitch7J"
    flop = #pixel
    brad = brad
}

and that is it now we have to finish the J formula and were done.  
Lets look at the J formula right now.

Ftswitch7J{
INIT:
LOOP:
BAILOUT:
DEFAULT:
Switch:
  type = "Ftswitch7M"

}

Wholely crud there's nothing there...what do we do now?

Lets populate the sections just like we did the m formula.

The init section will stay the same b and z need to be initialized.
Ftswitch7j{
init:
  b= @brad
  z=#pixel

In the loop section we need to change the #pixel entries to @flop

LOOP:
  z = @flop*b*z/(@flop^2+z^2)

The bailout section will stay the same.
Bailout:
  |z| < 4

The default section will remain the same.
Default:
Param brad
  hint = "this is the radius of the circle\
        That is tangent to the serpentine curve."
  Caption = "B in abz/(sqr(a)+sqr(z))"
  Default = (1.0,0.0)
endparam

The switch section is all that remains.
We know the name of the switch back formula
We don't need to send the flop value back
We do need to send the brad variable back.
Switch:
  type = "Ftswitch7M"
  brad = brad
}

So your J formula should now look like:

Ftswitch7J{
init:
  b= @brad
  z=#pixel
LOOP:
  z = @flop*b*z/(@flop^2+z^2)
Bailout:
  |z| < 4
Default:
Param brad
  hint = "this is the radius of the circle\
        That is tangent to the serpentine curve."
  Caption = "B in abz/(sqr(a)+sqr(z))"
  Default = (1.0,0.0)
endparam
Switch:
  type = "Ftswitch7M"
  brad = brad
}


Lets save our work.
    
Reload the M formula
Click the switch botton (the little arrow on top of the manle map) and
enjoy the julias this formula is excellent for finding weird julias.