Algodoo

Well done.

It's not thermal control that is modeled. It's material temperature change due to temperature changes in the surrounding air. For example, if you have a milling machine in your garage and the room temperature is regulated +/-5°F, then the milling machine material temperature fluctuation would be a fraction of the room temperature change. Thanks for the suggestions.
The filters in your heating system are for collecting dust.

I modified your scene on my PC as follows:
1. Unglued cars from sticks.
2. Connected cars to sticks with hinges (bend=true,bendConstant=100,bendTarget=whateverWor­ks,hingeConstant=1.0)
3.Set car collision layer to J.
4. Set car friction to zero.

Now the cars work like bumper cars. Try it you'll like it.

Q: Do the digit colors remind you of anything in particular?
A: Yes, now that you mention it, I can see that it's the resistor color code.

BTW, your Auto/Manual button is reversed, you click Manual to initiate Auto movement and vice versa.

Nice work.

Thanks guys. I think the physics of the roller ramp is similar to car drifting. I looked up "physics of car drifting", but don't see any statements mentioning the fact that the process is somewhat self regulating in that sideways friction preventing a spin out increases with sideways speed. In the roller ramp, for a fixed roller speed, the ramp apparent friction is proportional to the box speed.

Friction force is µ*N in the direction of relative motion, not in all directions. I'm thinking that the apparent coefficient of friction perpendicular to the direction of motion is zero, until you start moving in that direction, in which case the direction of motion changes.

Yes, that's what I think happens. Nice concise explanation. Now all we need is someone with a 3D printer to verify the physics.

Nice work.

I tried using AI to change the kids mood but I think that Xray's manual photo editing is much better.

I like the look of sheer terror on the baby's face. For some reason I find that comical. I must have watched too many Looney Tunes when I was younger.

Q: Could you explain a real world example of how this device is used?
A: No, because I don't know of any real world examples that use this concept. Same goes for design "B". I'm interested in simpler ideas for accomplishing the same task, ideas for improving the design, and reasons why the design might not work as intended. In design "A", the reaction of the tilted nut creates additional friction that subtracts from the available screw torque. I'm not absolutely certain it will work in real life.

P.S. The pivoting brake on design "A" is similar to the pivoting brake on a calk gun.

Thanks.

Nice visual effect and tight coding.

Puzzle: The marbles appear to be magnifying a virtual image directly under the marble. What is the texture matrix of the virtual image? What is the apparent magnification?

What is the texture matrix of the virtual image?
[0.62, 0.0, 0.635, 0.0, 0.7, 0.15, 0.0, 0.0, 1.0]

What is the apparent magnification?
[2.0667,2.3333]

This can be verified by setting the texture matrix for the main box to be [0.62, 0.0, 0.635, 0.0, 0.7, 0.15, 0.0, 0.0, 1.0] and textureClamped = [false, false].
To set a marble magnification to 1.0, set texture matrix = {[0.62, 0, pos(0) * 0.62, 0, 0.7, pos(1) * 0.7, 0.0, 0.0, 1.0]}.

A differential screw enables an effective thread pitch that would be impractical for a single thread. In other words, you get both precision and strength.

Differential Adjuster Screws
WORLD'S SMALLEST BORING HEAD

Q: LIKE THATS A BEAM NOT A STRING AND STRING IS STRING
A: I agree.

Thanks.

In general, I don't trust moving glued objects with scripting, but I tried it in this case and it appears to work fine. Thanks.

Some questions:
1. How do you configure each peg for a binary probability?
2. What are the units of the average?
3. What are the units of the standard deviation?
4. How well does this scene's distribution match the binomial distribution?

Thoughts:
In order to have perfect 50% probability, a ball would need to be exactly over the center of the peg and have vel(0)=0.0 at some point in time. If that were true the ball would end up perfectly balanced over the peg, so there needs to be some randomness in the calculations for the scene to work.

Here's what I think the answers to the questions are:

Q1: How do you configure each peg for a binary probability?
A1: I don't think there is a way to do it perfectly, although, after looking at all the other Galton board scenes, I see some scenes do a fairly good job (yours included).

Q2: What are the units of the average?
A2: The units are average balls/bin from your code.

Q3: What are the units of the standard deviation?
A3: It looks like bin count. I don't understand the formula. Do you have a source?

Q4: How well does this scene's distribution match the binomial distribution?
A5: The Chi-square goodness-of-fit test is often used to determine whether observed data fits a specific distribution, such as a binomial distribution. A simpler approach would be to put the outline of the perfect binomial distribution curve in your scene. I do neither in my scene.

Thanks. The formula is what I would expect, but I'm not sure if it's being applied correctly. I would expect a value to be applied to each bin like [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5] and a ball that falls in that bin would be assigned the value of the bin. The mean would be the sum of all the ball values divided by the number of balls. The standard deviation would calculated using the steps you mentioned above. I would expect the calculation to include n deviations, where n is the number of balls. The standard deviation units would be in terms of ball values or bin width. Your standard deviation calculation has a deviation associated with each bin ball count instead of with each ball. The calculation might be correct, but I'm not understanding it. It could be that both methods are correct and I'm just not seeing the second method.

Q: What do the red dots in each bin represent?
A: The red dot positions mark bar heights for a perfect binomial distribution curve.

Me:
I now see that the standard deviation calculation in this scene is incorrect since it does not take into account the relative position of the bin counts. The bin counts can be in any order and the calculation will yield the same result. Standard deviation is an indication of the "spread" of the data.

AI:
Ah, I’ve just realized something! The way we’re calculating the standard deviation here doesn’t quite hit the mark. You see, it’s not considering the relative positions of the bin counts. Funny thing is, we could jumble up the order of the bin counts and we’d still end up with the same result. But that’s not quite right, is it? After all, the standard deviation is supposed to give us a sense of how much our data is spreading out from the mean. Let’s see if we can fix this! 😊

Q: Would it also make sense to display the resulting number of balls in each bin after a run?
A: Yes. Thanks. I will probably do that at some point.

If you ask AI (MS Edge Copilot, for example): "Create a Python script that uses only the tkinter and random libraries to simulate a Galton board. Calculate the mean and standard deviation of the sample without using the statistics module." It will generate the logic and math necessary to run your scene. You would just need to translate the logic and math to thyme. The program that was created for me has only 33 source lines of code.

Q: When the "No. of rows" value changes, the "Ideal Std Dev" value changes immediately. Is that correct?
A: Yes. Ideal StdDev = (0.25*rows)^0.5

I wrote "ideal" because ideal is shorter than "perfect". I'm not even sure perfect is the best word. If you searched for "formula for standard deviation of a binomial distribution" then you will find the formula.