Fractals with interpreted interate and escape function

Translate

First part translates an formula from infix notation to postfix notation.

This tokens ...

binary_operator

% complex operators
dup (++) eq { tok_cadd }{
dup (--) eq { tok_csub }{
dup (**) eq { tok_cmul }{
dup (//) eq { tok_cdiv }{

% basic operators
dup (+)  eq { tok_add }{
dup (-)  eq { tok_sub }{
dup (*)  eq { tok_mul }{
dup (/)  eq { tok_div }{

unary_postfix_operator

% complex operators
dup (^^2) eq { tok_csqr }{
dup (^^3) eq { tok_ccub }{

unary_operator

% complex operators
dup (||)  eq { tok_cabs }{
dup (|/)  eq { tok_cria }{

... get translated into this postscript functions ...

/tok_cadd [5100 (complex_add)] def
/tok_csub [5101 (complex_sub)] def
/tok_cmul [5310 (complex_mul)] def
/tok_cdiv [5311 (complex_div)] def

/tok_csqr [7000 (complex_sqr)] def
/tok_ccub [7000 (complex_cub)] def

/tok_cabs [6000 (complex_abs)] def
/tok_cria [6000 (complex_ri_abs)] def

/tok_add [4110 (add)] def
/tok_sub [4111 (sub)] def
/tok_mul [4310 (mul)] def
/tok_div [4311 (div)] def

Configuration

( 1) /wh_point_step { 2 } def                %% x y step 
( 2) /wh_scale { 1 div floor cvi } def       %% scale whole image

( 3) /width  { 725 wh_scale } def            %% fractal width
( 4) /height { 450 wh_scale } def            %% fractal height

( 5) /center_y   -0.28 def                   %% x center of view in complex area
( 6) /center_x   0.72 def                    %% y center of view in complex area
( 7) /zoom       32 def                      %% zoom level of view

( 8) /color_map       (default) def          %% definitions from colors directory
( 9) /iterate_maximum 100 def                %% recusion escape value
(10) /limit_value     4   def                %% limit of z

(11) (z ^^2 ||) tokenize parse codegen
     /limit_formula exch def

(12) (z ^^2 -- c) tokenize parse codegen
	 /iterate_formula exch def
    </code>

tokenize

Separates the input string into tokens. A token is an 2 dimensional array consisting of a tok_id and a text. The tok_id is also interpreted as an operator precedence, which is important for the parse process.

(z ^^2 ++ c) tokenize
[10 (z)] [7000 (complex_sqr)] [5100 (complex_add)] [10 (c)]

parse

Parses the tokens into a syntax tree representation.

[10 (z)] [7000 (complex_sqr)] [5100 (complex_add)] [10 (c)] parse
[10 (z)] [7000 (complex_sqr)] [10 (c)] [5100 (complex_add)]

codegen

Translates the calculus operations into postscript functions. The postscript functions are located in lib/complex.ps

[10 (z)] [7000 (complex_sqr)] [10 (c)] [5100 (complex_add)] codegen
(zr zi complex_sqr cr ci complex_sub)

Point Step

Color Map

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Makefile

Important goals: mb cbs color_test test

make mb
make cbs
make color_test
make test

Color Test