Macdonalds Law: Increasing cosmological constant with time, a property of an expanding fractal

Cosmic Increasing Acceleration of Cosmological Constant or Dark Energy with Time Explained by the Fractal

Update 2025 10 06

I spent the last two days reviewing the commentary on the changing cosmological constant and examining the papers. As a consequence, I would like to retract my previous update, as it is incorrect. My original post remains correct, to the best of my knowledge. The more I examine it, the more it aligns precisely with my model's predictions.

What am I to do? Maybe I need to write another short paper bringing these two 'things' together. 

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Update 2025 09 29

I would like to update what I have written below, as I may have it incorrect.

It looks like it's the opposite, actually. Sadly for me, the rate of change is greater now than it was in the past, and that is what it's been saying along, and I misinterpreted that.

The one thing I can take from this is a look at my own character. When I saw it, I had misinterpreted this. I took it on board quickly and realised that what I had claimed was wrong. It's important to correct this, and so I'm doing this now. But I'll keep the post up, and I see it as part of my character; I hope you do too.

What does this mean for my fractal model? I don't know. It is not what I expect to see, but that many other properties are observed still keeps me interested, and I hope you too.

Original post:

I think I may have discovered a law of nature. And in my own little room here .. with my cat, I'm calling it Macdonald's law. (m a c, small d). lol!

In my fractal model of the universe, which I published a couple of years back, one of the predictions is that the acceleration rate will increase with time, the further we look out to its origins. This is an inextricable aspect of fractal growth. 

Over the last month or so, I have been reading the new discoveries made by the modern telescopes, that they are observing changes in the accelerated rate of the universe, and that the 'dark energy', the 'cosmological constant', may change over time. That it was stronger in the past! https://www.scientificamerican.com/.../why-evolving-dark.../
When I first read this, I interpreted it as working against my model, and I just swallowed it as something that I can't explain and not what I expected, and it was a little disappointing. (..you have other things to do, move on, Blair)

Two nights ago, I reread and focused in on them again, and I realised that I may have my interpretation wrong and that these new discoveries do not contradict my model but are precisely what I expect or predict.

My model already demonstrates Hubble-Lemaitre expansion, accelerated expansion, and now a changing rate of acceleration. It also predicts the distribution and demographics of galaxies. See image. Note that the bottom graph shows increasing acceleration with time.

Don't worry, I can't make sense of it either (yes, i can), it is crazy stuff, but the geometry does it. All I've done is taken measurements on the growth of a known geometry, the fractal. Nothing special, really; anyone could do it. But I've applied it to everything, including the universe itself.

What to do now?
I intend to write to the journal's editor and request a discussion.

I'll keep you in touch.

The above graph in my image is from a YouTube clip in which observations are used to argue that the universe is not fractal. The WiggleZ team argues that the universe is fractal, but only within the pink box in the diagram—out to half 1 billion years. It shows the distribution of galaxies is high and fractal structured in small scales but smooth and non-fractal at large scales. I argued, from my model, that that is what you would expect to see in a growing fractal.
The second and third graphs are directly pulled from a mathematical model analysing velocity with distance and acceleration with distance when observed within a growing fractal.

In other words, think of a tree—that is what I have basically modelled. A tree is a fractal.  The crosses on the graph represent the size of branches. The cross to the far right represents the size of the tree's trunk. So, each branch size accelerates away from the other size as the tree grows. And this has actually, in studies, been shown to be true.