how can i model such a plot in autocad.this plot what created using a mathematical formula ,demostrated in mathlab.thanks

The equations would be necessary.... That looks like some kind [two kinds, really] of formula in which the angle to a point on the curve is based on the inverse of a trigonometric function whose value swings between positive and negative without ever going to infinity [such as sine or cosine], applied to some multiplier of the local radius, and for the browner curve with a constant angle [looks like 45 degrees] added to the result.  That shouldn't be very hard to work out -- for a related routine that draws polynomial functions [y = ax^n + bx^(n-1) + .... + px^2 + qx + r], see my PolynomialFunction.lsp routine, available here.  But this one, being radial, would not involve X and Y coordinates, but instead (polar) functions measured from the origin as basepoint, in a (repeat) function stepping through small increments of radius as the distance arguments, and calculating the angle arguments for each based on the equation, and presumably used in a SPLINE, or perhaps a POLYLINE that you could spline-curve to smooth it out.

You can use our 2DPLOT utility (see http://www.cadstudio.cz/en/apps/2dplot/). You equation then should be expressed in cartesian space (X/Y): ; for range (0-1.5>(defun fPolar1 (u / r tau alfa R0);x = (* r (cos th));y = (* r (sin th)) (setq r u) (setq tau 1.1) ; example (setq alfa 1.0) ; example (setq R0 0.1) ; example (setq th (* alfa (sin (/ (* pi (log (/ r R0))) (log tau))))) ; your expression (list (* r (cos th)) (* r (sin th))) ; return (X Y))Then call: (2Dplot fPolar1 0.001 1.5 0.001) meaning - draw my function "fPolar1" from 0.001 to 1.5 (the radius), with ministeps of 0.001 

Another, (polar)-based, solution (along with Vladimir's solution above) is over here. See also other Posts in that same thread.

EDIT:  That link doesn't seem to work.  Try copy/pasting this:https://forums.autodesk.com/t5/autocad-2013-2014-2015-2016-2017/modeling-a-mathematical-shape/m-p/6886507#M163554Kent Cooper2017-02-17 21:02:37