Thank you very much for this very much needed guide.

I'm glad you found it helpful.

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*Ultra-Fractal
*Apophysis
=ImagersFractalDDs

Brillant

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*Apophysis
*FractalDreams
~revolutionfractals <---NEW CHECK 'EM OUT!

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*Ultra-Fractal
*Apophysis
=ImagersFractalDDs

Ah, this is what I've never had the time and/or motivation to do

I have not read the whole thing in detail, but I did notice that your final transform description is not right. "Essentially, after all the points have been plotted, they are passed through the Final Transform’s function." You've got this backwards. If the current iteration of the chaos game gives (x,y) then the point F_final(x,y) is plotted and (x,y) is fed back into the chaos game. The final transform modifies only the plotted points, not the points that are fed back into the chaos game.

Are you really just 17?

Yep, I'm just sort of an insomniac, and thinking of mathematical concepts helps me get to sleep.

As for your problem with the Final Transform description, it isn't wrong. What I meant by my wording is that after you plot every point you pass them all through the Final Transform. That is to say, when plotting points the Final Transform has nothing to do with anything, and then when you're done you use it to transform the points.

Now, technically that's not how the program does it, because internally it actually creates a separate action which computes the Final Transform's effect on each point as their plotted, however for the purpose of explanation I figured it was easier to explain it that way.

Plus, I used the word "essentially", and while I might abuse those sort of prepositions in my normal speech, I try to shy away from them unless it's totally necessary.

My next document-project is going to be on Complex Analysis and how many Apophysis is related to that, but after that I'm thinking of redoing this and making it a bit clearer. (it isn't quite as glamorous as I first envisioned it)

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*Ultra-Fractal
*Apophysis
=ImagersFractalDDs

By the way, thanks for the two s. I always feel awkward responding to someone and then going to their main page and posting something separate.

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*Ultra-Fractal
*Apophysis
=ImagersFractalDDs

Nice! I'm just jumping into fractals, and this was a good read. I was wondering how the basic math behind it worked, and it's not so arcane as I had thought. This also explains why the pixels dance every time you reload the preview on a fractal.

On the side, nice avatar. And you're a year older than I am. Cheers!

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Have you ever had a moment
when everything was clear
and then were cursed to find a flaw
and find yourself in fear?

Is a troubled future
of flaws in truth a bet?
Or is it simply by our nature
that truths are true and we forget?