The photo of the 'egg' stage of Mutinus in my book didn't come out as well as I hoped. However, this time I labelled the various parts so it is easier to see what happens. Under the right conditions it takes about half an hour for the stinkhorn to go from the egg stage to fully mature (click here). You can see the compressed tissue of the central columella. This tissue absorbs water rapidly, the cells swell, and the stalk expands and breaks through the outer wall (peridium) to become the stalk of the mature stinkhorn. As this is happening, enzymatic activity and growth pressure cause the spore mass (green) to mix with the gelatinous material that sheaths the head and this mixture liquifies into a smelly goo that covers the bright red cap of the stinkhorn. The tissue in the cap is already expanded (i.e. is apparently less compressed than the tissue of the stalk). Thus, the head in the mature fruitbody is about the same size as it is in the egg. The egg is about 2 cm tall.
In NA this species (Mutinus ravenelii) is commonly called the 'Dog Stinkhorn' but should perhaps be called the 'Red Stinkhorn' as it is named in Europe or perhaps Ravenel's Stinkhorn. The Dog Stinkhorn has a slender, whitish stalk and is usually taller than the Red Stinkhorn.