How to visually show a game of Roulette as a fractal?

[falkor2k15]

I've been pondering this one just now. Will test and see if I can make a nice fractal pattern using Roulette, but would welcome any suggestions to add perspectives on how we might achieve this or why it's not possible?

[Gitano]

Hi,
nice idea, I'm just searching on the net some programs to do awesome fractals, but I didn't find one with random numbers to fulfill..
Try "Apophysys" to download, it's nice [/url][/img]

[Gitano]

..and the house win with 0 green ?!?

[falkor2k15]

OK, so we know a fractal can be developed from a few rules that draw lines based on the roll of a dice - each line drawn from the point where the previous line finished. And between the pattern formed by the lines is an empty space:


So my program plots the roulette number of the defining dozen whenever a dozen cycle closes. The defining dozen is then carried over to the next cycle, and there's 63% the next cycle will be defined by the same dozen. And it seems after the end of 10 number cycles there is generally an empty dozen. Since the 10 cycle sets selected here begin with number 2 (dozen 1), there's more chance the empty dozen will be dozen 2 or 3. 


I just need to add the lines now.

[falkor2k15]

Copyright © 2019, Falkor

[Bigbroben]

Falkor,
maybe if the nrs were laid out in a circle, actually just like the wheel's layout, perhaps there would more chances of seeing a fractal taking shape...

[falkor2k15]

I think some  new information can be gleaned from the above analysis:
The defining dozen seems to dominate for a period of time, and so does the top 2 dominant front runners - seem to keep their lead for extended periods.
For the dominant front runners, when it's their turn to dominate we tend to get a repeat on the individual numbers that were defined under previous defining dozens.

For example, the top most dominant dozen that won the sets above by covering the most numbers within a single dozen also had the most repeats on those individual numbers:
4, 2, 3
2, 3, 11, 10, 1
10, 9, 12, 8
5,22
2,9,1,6,11,4

[Bigbroben]

Here we go... Fractals.

Not giving a system here, just thoughts for the moment.
Let's forget about EC for the moment, for my idea is not relevant to them.

Ok: fractal: a pattern that repeats itself not on the same plane, but on a lower or higher plane ( bluntly said).  This of a broccoli or an elm...

Doz and columns offer a first alternating choice, just like 3-phase electricity.  Put 123 in a circle and you can go, from spin to spin, cw or ccw.
Put double streets in a circle: you can go cw or ccw, jumping to the next or jumping over some.
Same then for streets: put them in a circle.  You can go cw or ccw, jump to the next or jump a few.
So on for splits, single nrs (not sure about corners, they're hard to define).

Can we now suppose a fractal could first show itself on a higher plane (doz or DS) and repeat on a lower plane, maybe not exactly the same, but similarly?

When to call a pattern ''fractal''? Once it shows on 2 planes? or more?
How likely is a ''2-plane'' pattern to go on for a third plane?
How to recognize it? 
How often can the same ''3-plane pattern'' appear in a short range?
How specific must the behavior be?

Of course,  fractals can be seen in another way, this was a brainstorming idea.

Sleep on it.

[Steve]

Here's a start:
link:s://natureofcode.com/book/chapter-8-fractals/

[Firefox]

For me roulette is too random to be represented by regular fractal models. As I understand it, the branching ocurrs in a semi-regular fashion. If you look at images of fractal generation they appear very regular and symmetrical.

Whereas if you take say dozens, one can appear 6 times in a row. It's a 1 in few hundred event. This kind of fluctuation would provide a lot of distortion to the pattern locally, so any modelling would need to represent that volatility.