Families of curves, colour filled

A favourite coding activity for me is generating unusual mathematical figures and playing with the parameters. Many have traditional names, and I'd just found a reference page with several that were new to me.

Curves to display in 2D are usually in Cartesian ( x, y) coordinates, or polar ( r, theta). I've variations on the following code for generating coloured families of trochoids, cycloids, cochleoid, trifoliuM, sextic, Fermat spiral, etc. Using colour sequential fills and adding progressive rotations produces eye-catching graphics.

Code 


    '  ratchet curve


    nomainwin

    pi      =4 *atn( 1)

    Cx  =251    '   centre to fill from
    Cy  =251
    r   = 30    '   Initial colour values for the fill.
    g   =260
    bl  = 20

    WindowWidth  =500
    WindowHeight =550

    open "Ratchet pawl" for graphics_nsb as #wg

    hw      =hwnd( #wg)
    calldll #user32, "GetDC", hw as ulong, hdc as ulong

    #wg "trapclose quit"

    #wg "home"

    state$ ="up"

    for a =140 to 10 step -2


        re          =int( 128 +128 *cos( a /7))
        gr          =int( 128 +128 *sin( a /19))
        bl          =int( 128 +128 *cos( a /37))

        fillCol$    =str$( re)     +" " +str$( gr)   +" "   +str$( bl)

        #wg "color ";     fillCol$
        #wg "backcolor "; fillCol$

        targetcolor   =bl *2^16    +gr *2^8    +re      '   this is colour to fill WITH
                                                      '   this is also the colour of the outline to fill out TO.

        for theta =0 to 2 *pi +0.002 step 0.001
            scan
            r   =  a +int( ( ( 1.5 *( theta)) mod pi) *( a /5))
            x   =250 +r *cos( theta +a /130)
            y   =250 -r *sin( theta +a /130)
            if state$ ="down" then
                #wg "goto "; int( x); " "; int( y)
            else
                #wg "goto "; int( x); " "; int( y)
                #wg "down"
                state$ ="down"
            end if
        next theta

'goto [skip]
        calldll #gdi32, "ExtFloodFill",_
            hdc                as ulong,_
            Cx                 as  long,_
            Cy                 as  long,_
            targetcolor        as  long,_                '   ie fill out 'til this colour is met..
            _FLOODFILLBORDER   as  long,_
            result             as  long
[skip]
    next a

    #wg "getbmp scr 0 0 500 500"
    bmpsave "scr", "ratchet6d.bmp"

    wait

    sub quit h$
        calldll #user32, "ReleaseDC", hw as ulong, hdc as ulong, ret as void   'release the DC
        close #wg
        end
    end sub