JSFiddle - React, Tailwind, and code Playground

HTML

<div id="homeimg">
    <img src="http://placehold.it/150/ff00ff&text=1"/>
    <img src="http://placehold.it/150/ccaaff&text=2" style="display:none" />
</div>

CSS

img {
  position:absolute;
}

JavaScript

$(document).ready(function () {
       $('#homeimg img:first-child').addClass('activeimg');
       setInterval(cycleMe, 4000);
       // get an array of your images
       var arrImgs = $('#homeimg img');

       function cycleMe() {
           var currImg = $(arrImgs[0]);
           var nextImg = $(arrImgs[1]);
           // You can do this with simple array splicing and pushing
           nextImg.fadeIn(1500);
           currImg.fadeOut(1500, function () {
               currImg.removeClass('activeimg');
               nextImg.fadeIn(0).addClass('activeimg');
               // remove the first item from the array
               arrImgs.splice(0,1);
               // add it to the end of the array
               arrImgs.push(currImg);
           });
       }
   });