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#N canvas 648 0 632 537 10;
#X obj 21 109 @complex_sq;
#X text 176 59 this object computes the square of complex numbers.
if seeing imaginary as Y and real as X \, then this operation squares
the distance of a point from origin and doubles the angle between it
and the +X half-axis clockwise. :);
#X floatatom 21 58 5 0 0 0 - - -;
#X floatatom 21 188 5 0 0 0 - - -;
#X floatatom 64 58 5 0 0 0 - - -;
#X floatatom 58 188 5 0 0 0 - - -;
#X obj 21 78 #pack;
#X obj 114 185 #print;
#X obj 21 159 #unpack;
#X obj 103 488 # +;
#X obj 133 488 # abs-;
#X obj 3 488 doc_also;
#X obj 181 488 # C.sq-;
#X obj 3 324 doc_c 0;
#X obj 3 364 doc_i 1;
#X obj 3 426 doc_o 1;
#X obj 0 0 doc_h;
#X obj 14 456 doc_oo 0;
#X obj 14 394 doc_ii 0;
#X obj 97 394 doc_m i0 grid;
#X obj 97 456 doc_m o0 grid;
#X text 232 394 grid of size (... \, 2);
#X text 232 456 grid of same size;
#X obj 0 508 doc_f;
#X text 178 128 However \, this (old) object is backwards from the
rest of GridFlow because it puts Imaginary before Real. [#fft] puts
the Real part first. Open this abstraction to discover the new way
to square a complex number. (The extra multiplication is the net result
of swapping components before and after the squaring);
#X text 178 212 used on an indexmap (#remap_image) \, this makes each
thing appear twice \, each appearance spanning half of the original
angle. straight lines become hyperbolic \, etc.;
#X text 179 259 In the original version of GridFlow (aka Video4jmax
0.2) \, the first example patch was feedback_fractal \, which used
this operation with a [#remap_image] \, though it was expressed in
much different terms back then.;
#X connect 0 0 7 0;
#X connect 0 0 8 0;
#X connect 2 0 6 0;
#X connect 4 0 6 1;
#X connect 6 0 0 0;
#X connect 8 0 3 0;
#X connect 8 1 5 0;
#X connect 11 1 9 1;
#X connect 11 1 10 0;
#X connect 11 1 12 0;
#X connect 19 1 21 0;
#X connect 20 1 22 0;
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