Here is a link to a web page with an image:

I used the Epicycloid_Mset formula to make this image. The thickness of the curve is adjusted to be so thick that the curve is filled in and turned into a "lily pad".

The parameter file used to make this image is below:

Autumn_Lilypads { ; Exported from Fracton.

 reset=2004 type=formula formulafile=fracton.frm

 formulaname=Epicycloid_Mset passes=1 float=y

 center-mag=-0.736775091553311/0.2424716796875001/1\

 33.333335/1/0/0

 params=0.04/0.15/5/30/8/0.25/0/0/0/0 maxiter=500

 inside=255 outside=summ

 colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\

 zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\

 z88 }

frm:Epicycloid_Mset {

; Epicycloid_Mset based on Astroid_Mset

; Astroid_Mset copyright (c) Paul W. Carlson, 1997

; Epicycloid_Mset by Mike Frazier, 2011

;****************************************************

; Always use floating point math and outside=summ.

;

; Parameters:

;   real(p1) = a factor controlling the width of the curves

;   imag(p1) = radius of the curve

;   real(p2) = number of color ranges

;   imag(p2) = number of colors in each color range

;   real(p3) = number of cusps, even integers

;   imag(p3) = cusp amplitude (0 to 1)

;

; Note that the equation variable is w, not z. 

; Initialize cindex to the index of the background color

; Formula modified to avoid color index 0 which can not

; be used with outside=summ in FractInt v20.04

;****************************************************

w=0,

c=pixel,

z=0,

cindex=254,; Background color

bailout=0,

iter=0,

range_num=0,

i=(0,1),

r=imag(p1),

f=real(p3)+1,

b=imag(p3),

;****************************************************

; In the accompanying par file,

; we have 8 color ranges with 30 colors in each range

; for a total of 240 colors. The first range starts at

; color 1.  Pixels will use color 254 when |w| > 1000.

; Other values can be used here as long as the product

; of num_ranges times colors_in_range is less than 255.

; Color 254 is reserved for the background color and 

; color 255 can be used for the inside color.

;****************************************************

num_ranges=real(p2),

colors_in_range=imag(p2),

;****************************************************

; Real(p1) controls the width of the curves.

; These values will usually be in the range 0.001 to 0.1

;****************************************************

width=real(p1),

index_factor=(colors_in_range-1)/width:

;****************************************************

; The equation being iterated.  Almost any equation

; that can be expressed in terms of a complex variable

; and a complex constant will work with this method.

; This example uses the standard Mandelbrot set equation.

;****************************************************

w=w*w+c,

;****************************************************

; The orbit trap curve is an epicycloid.

; Any two-dimensional curve can

; be used which can be expressed in parametric form in

; terms of the angle from the origin.

;****************************************************

ang=atan(imag(w)/real(w)),

astroid=r*(cos(ang)-b*cos(f*ang)+i*(sin(ang)-b*sin(f*ang))),

;****************************************************

; If the orbit point is within some distance of the curve,

; set cindex to the index into the colormap and set the bailout

; flag.  Note: the way we use the "distance" here has

; the effect of turning the curves inside-out in the image.

;****************************************************

distance=abs(|w|-|astroid|),

if(distance<width&&iter>1),

cindex=index_factor*distance+range_num*colors_in_range+1,

bailout=1,

endif,

;****************************************************

; Cycle through the range numbers (0 thru num_ranges - 1)

; With two color ranges, even iterations use color

; range 0, odd iterations use color range 1.

;****************************************************

range_num=range_num+1,

if(range_num==num_ranges),

range_num=0,

endif,

;****************************************************

; Since we are using outside=summ, we have to subtract

; the number of iterations from z.

;****************************************************

iter=iter+1,

z=cindex-iter,

;****************************************************

; Finally, we test for bailout

;****************************************************

bailout==0&&|w|<1000

}