The original author of the article on MSE, jimjames, has now created a post on that thread which does show the effect of re-investing dividends.
What I will say, though, is that re-investing dividends is quite different to the point made in the last sentence of the first post on the thread, i.e. that fluctuations in the value of the capital should be less of an issue if the primary concern is for the income - in which case, the investor should be more concerned both with the reliability of the level of income and its rate of growth, which ideally should match the investor’s personal rate of inflation, i.e. the rate at which their own annual expenditure rises. And assuming that their capital does not get depleted to zero in the process!
Once you do start talking about re-investing then you’re into a different ball game, namely Total Return investing. Here, both the level of income and its growth rate can take a back seat because the longer term aim is for the capital to grow in value. ‘Why?’ did I hear somebody say? 'When we all know that a good proportion of the long-term returns from equities is from the dividends being re-invested.. For the simple fact that when a dividend is re-invested, it ceases to be a dividend and instead becomes capital - so in this case the value if capital is more relevant, However, so long as the trend in value is upwards, the volatility in its value should be less of an issue - except towards the end of the investment timescale when a sudden lurch downwards of 10-20% might cause a few palpitations (although I am wandering into ‘drawdown’ territory here).