Mandelbrot set outline for Babbage Analytical Engine

mandelbrot.ae

    Mandelbrot set outline

    This program does not use precomputed points.
    It samples the complex plane, runs the Mandelbrot
    iteration z = z^2 + c at each sample, and plots
    points in the sampled region, runs the Mandelbrot
    iteration z = z^2 + c at each sample, and plots
    every point that remains bounded after the chosen
    iteration limit.  This produces a dense image of
    the set that fills the Curve Drawing Apparatus.

A set decimal places to 15
A write numbers with decimal point

    Sampling window and resolution

N100 -2.20              . x start
N101 0                  . x index
N102 0.025              . x step
N103 -1.20              . y start
N104 0                  . y index
N105 0.025              . y step
N106 30                 . max iterations
N116 130                . x sample count
N117 98                 . y sample count

    Constants

N107 0
N108 1
N109 2.0
N110 4.0
N111 0.575              . x centring offset
N112 0.615384615384615  . x plot scale
N113 0.816326530612245  . y plot scale
N114 10000000000        . plotter fixed-point scale
N115 0.010              . half-height of sample tick mark

    Working storage

. N120                  . c real
. N121                  . c imaginary
. N122                  . z real
. N123                  . z imaginary
. N124                  . z real squared
. N125                  . z imaginary squared
. N126                  . next z real
. N127                  . next z imaginary
. N128                  . magnitude squared
. N129                  . iteration counter
. N130                  . escaped flag
. N131                  . inside flag
. N133                  . current plot x
. N134                  . current plot y
. N137                  . x offset
. N138                  . y offset

DC Blue

(?

    c imaginary = y start + y index * y step

*
L104
L105
S138

+
L103
L138
S121

+
L107
L107
S101                    . x index = 0

(?

    c real = x start + x index * x step

*
L101
L102
S137

+
L100
L137
S120

    Reset Mandelbrot iteration state for this point

+
L107
L107
S122                    . z real = 0
S123                    . z imaginary = 0
S129                    . iteration counter = 0
S130                    . escaped flag = 0

    Iterate z = z^2 + c until escape or iteration limit

(?

-
L107
L130
{?

*
L122
L122
>
S124

*
L123
L123
>
S125

+
L124
L125
S128                    . magnitude squared

-
L128
L110
{?

+
L108
L107
S130                    . escaped = 1

}{

*
L122
L123
>
S127

*
L127
L109
>
S127

+
L127
L121
S127                    . next z imaginary

-
L124
L125
S126

+
L126
L120
S126                    . next z real

+
L126
L107
S122

+
L127
L107
S123
}
}

+
L129
L108
S129

-
L129
L106
)

    A point is considered inside if it never escaped

-
L107
L130
{?
+
L108
L107
S131
}{
+
L107
L107
S131
}

    Map the sampled complex-plane point into plotter space

+
L120
L111
S133

*
L133
L112
>
S133

*
L121
L113
>
S134

    Plot every point classified inside the set as a short tick

-
L131
L108
{?

*
L133
L114
DX

-
L134
L115
S128

*
L128
L114
DY
D+

+
L134
L115
S128

*
L128
L114
DY
D+
D-
}

+
L101
L108
S101                    . x index += 1

-
L101
L116
)

+
L104
L108
S104                    . y index += 1

-
L104
L117
)

A write annotation Mandelbrot outline complete
A write new line