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exp-Kepler.lisp
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;; -*- Mode:Lisp; Syntax:ANSI-Common-LISP; Coding:us-ascii-unix; fill-column:158 -*-
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;; @file exp-Kepler.lisp
;; @author Mitch Richling <https://www.mitchr.me>
;; @brief Draw Newton-like fractal and output to a TGA file.@EOL
;; @std Common Lisp
;; @copyright
;; @parblock
;; Copyright (c) 2012,2015, Mitchell Jay Richling <https://www.mitchr.me> All rights reserved.
;;
;; Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
;;
;; 1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
;;
;; 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation
;; and/or other materials provided with the distribution.
;;
;; 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software
;; without specific prior written permission.
;;
;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
;; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
;; LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
;; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
;; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
;; DAMAGE.
;; @endparblock
;; @filedetails
;;
;; Kepler's equation is
;;
;; $$M = E - e\cdot\sin(E)$$
;;
;; We fix $M=1$, the mean anomaly, and $e=0.083$, the eccentricity. Newton's method can then be used to solve for $E$, the eccentric anomaly.
;; While $E$ is always a real number in celestial mechanics applications, we consider her the case of a complex valued $E$ and draw Newton-type
;; fractals.
;;
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(declaim (optimize (speed 3) (safety 0) ( debug 0) (compilation-speed 0)))
(defun drawNewtonFract (x0 y0 x1 y1 out-file max-z max-d max-c sfac xmax ymax col-method fdf)
(let ((dquad (mjr_fsamp_dq-func-r123-color (lambda (x y)
(loop with ctr complex = (complex (/ (+ x0 x1) 2) (/ (+ y0 y1) 2))
for (tv bv) (complex complex) = '(#C(1.0 0.0) #C(1.0 0.0)) then (funcall fdf z)
for z complex = (complex x y) then (if (mjr_chk_!=0 (abs bv)) (- z (/ tv bv)) 0)
for zd short-float = (abs (- ctr z))
for cnt fixnum from 1
for fv = (cond ((<= max-d zd) (vector 0 0 255))
((<= max-z (abs z)) (vector 0 0 150))
((< max-c cnt) (vector 0 0 100))
((mjr_eps_=0 tv 1e-3) (let ((cm1 (case col-method
(:col-itr (mod (* sfac cnt) 255))
(:col-maxd (truncate (mod (* sfac zd) 255) 1)))))
(vector (- 255 cm1) cm1 0))))
do (if fv (return fv))))
:ano-typ :ano-typ-truvec
:xdat (list :start x0 :end x1 :len xmax)
:ydat (list :start y0 :end y1 :len ymax))))
(mjr_tga_from-dquad out-file dquad :data "c")))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(time (drawNewtonFract -66.5 0.2 ;; x0 y0 | -0.5 2.7 | -66.5 0.2 |
-59.5 8.2 ;; x1 y1 | 0.4 3.6 | -59.5 8.2 |
"exp-Kepler-OUT-3.tga" ;; out-file
90.0 ;; max-z
95.0 ;; max-d | 50.0 | 95.0 |
40 ;; max-c
130 ;; sfac
30 ;; sfac
(expt 2 9) ;; xmax
(expt 2 9) ;; ymax
:col-itr ;; col-method
(lambda (z) ;; func and diff
(declare ((complex (short-float)) z))
(list (- z (* #C(0.08 0.0) (sin z)) #C(1.0 0.0))
(- #C(1.0 0.0) (* #C(0.08 0.0) (cos z)))))))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(time (drawNewtonFract -66.5 0.2 ;; x0 y0
-59.5 8.2 ;; x1 y1
"exp-Kepler-OUT-4.tga" ;; out-file
90.0 ;; max-z
95.0 ;; max-d
40 ;; max-c
130 ;; sfac
(expt 2 11) ;; xmax
(expt 2 11) ;; ymax
:col-maxd ;; col-method
(lambda (z) ;; func and diff
(declare ((complex (short-float)) z))
(list (- z (* #C(0.08 0.0) (sin z)) #C(1.0 0.0))
(- #C(1.0 0.0) (* #C(0.08 0.0) (cos z)))))))