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;; @file      exp-ODElorenzEuler.lisp
;; @author    Mitch Richling <https://www.mitchr.me>
;; @brief     Compute and draw the Lorenz strange attracter without :MJR_ODE..@EOL
;; @std       Common Lisp
;; @copyright 
;;  @parblock
;;  Copyright (c) 2011,2015, 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
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(let* ((max-balls 30000)
       (x-dat     (make-array max-balls))
       (y-dat     (make-array max-balls))
       (z-dat     (make-array max-balls))
       (t-dat     (make-array max-balls)))
  (loop with delta = 0.003
        with x0    = 0.1
        with y0    = 0.0
        with z0    = 0.0
        with a     = 10.0
        with b     = 28.0
        with c     = (/ 8 3.0)
        for cur-bal from 0 upto (1- max-balls)
        for x = x0 then (+ X (* A (- Y X) DELTA))
        for y = y0 then (+ Y (* (- (* X (- B Z)) Y) DELTA))
        for z = z0 then (+ Z (* (- (* X Y) (* C Z)) DELTA))
        do (setf (aref x-dat cur-bal) x
                 (aref y-dat cur-bal) y
                 (aref z-dat cur-bal) z
                 (aref t-dat cur-bal) (* cur-bal delta)))
  (mjr_vtk_from-dsimp  "exp-ODElorenzEuler-OUT2.vtk" (mjr_dsimp_make-from-xyz :xdat x-dat :ydat y-dat :zdat z-dat
                                                                              :connect-points 't
                                                                              :data-vectors t-dat :data-vector-names "time")
                       :simplices 1))