How life grows exponentially 

This channel is just a treasure buried in the sea that is youtube. I hope you don't stop uploading videos and that your channel grows to infinity. Superb content, just astounding, terrific.

Finally the RU-vid algorithm suggests some really nice channels. Like this one. Just one video watched and subscribed. Quality beats quantity. This how it should be.

Can we just talk about how this man not only made a very very very minor error in part of one of his past videos and is apologizing for it, but the fact that he apologized better than any youtube apology video ever. Like, I wasn't even disappointed or upset that he made that mistake, yet, I feel inclined to accept the apology for something that doesn't even need one. I must say, props to you Primer! Keep up the amazing content!

Man, when those simulations mapped perfectly onto the exponential prediction I got the chills...maths truly is the language of the universe!

Please upload more frequently! You have no idea how impatiently I waited for this second video!

2040: So now we will be teaching our blobs how to apply quantum physics in everyday life.

Equilibrium; perfectly balanced as all things should be....

Let's just all admire the animation skill that went into making this video

Life: No one understands me, I'm an unsolvable mystery!!! Primer: Hold my blob.

I'll never understand why people would dislike videos like this. Then I remember the words "statistical fluctuations" and I feel safe again

Well brother, this channel is gona soon to touch million subscribers i.e. by high replication inducing quality videos

Good video man, I'm loving this framing of creating a mathematical model of evolution. Keep up the good work :)

Man I want to play with this sim. You could develop it into a game

It was weird to realize there were only like 10 videos on this channel, this just seemed like a channel that would have dozens if not hundreds of these little educational simulations I love!

This is really good content, hope to see more of it in the future.

Those videos are so informative ! Hope more people will get to discover and learn from them.

I love how subtly you’re introducing concepts of differential equations without actually getting into DE’s. Complex topics explained so simply.

holy cow this is so soothing??? Subscribed and excited for more!

If anyone is confused about how the growth rate translates into a population graph, take note that the growth rate equation is a differential equation y' = B + (R - D)y. If you work out the math for it, you will find that the population equation is y = B / (D - R) + ce^(R - D)t, where t is time and c is some constant. Note that y is actually a family of functions, so there are infinite possible equations that fit this curve with different c values. To find c, we would need to know the value of y at some time t. If we assume the population is 0 at t=0, then c = - B / (D - R) = B / (R - D). It doesn't really matter that much though. We can explore the three cases of D > R, D = R, and D < R using this equation. If D > R, then the exponential term has a negative exponent. A property of such exponential terms is that they approach 0 as t goes to infinity. This leads to the equilibrium state described in the video, where the population will stabilize at B / (D - R) individuals. If D = R, then the curve is flat at B / (D - R) + c. If D < R, then you get a positive exponent and exponentially increasing growth.

Came from 3B1B, stayed for the great content.

I've never thought about those simple relations, that can produce radically different behaviors. Thank you! The evolution model is going to be interesting. Looking forward to the next episode.

You do this amazingly well, it so easy to understand. The graphics are nice and the graphs are easy to read. Very impressed, good content 10/10.

I only found your channel today but it is truly a hidden gem of RU-vid! I’ve already watched like 8 videos and am subscribed. Great content!

I love the background music it makes me chill so much while learning more about life, thanks Primer blob, keep up the good work!

I’m looking forward to the rest of this series. Good job!

Holy shit, how is content this good this unknown? God damn

I love your channel never quit!

Your Videos are amazing! Keep it going.

If I told my child self that my future would be sitting in front of a screen watching blobs populate instead of a higher purpose, I would be surprised too

Excellent videos! Loving your series

Man, I love this channel! Please continue making videos!

Just found this amazing channel, i love this type of content!!!!

I watched one video and I subscribed, this channel is awesome, hope you keep making these videos.

I just discovered this channel and it's just amazing!

His voice is just so soothing and calming. Makes even the difficult topic less daunting

I love your series ! ... the content, animation and tune in the background ...

Totally just realized while watching that this could be nicely modeled with a Markov chain. Are you going to get into higher-level stuff like that later, or stick with these basics? Thanks for the video - really cool channel, I'm excited to see where it goes! Subscribed.

The music is so good as well. What a pleasure to wstch

I love this channel, keep it up👍🏻

Awesome content bro.Please keep uploading

I've watched several of these for the past couple of months, and everything you day makes more sense than any of my classes

Literally the best channel I have come across since stampycat when I was 8

I feel like you could use this series as an introduction to calculus. Great videos ! :)

amazing series :D I love the animation !

Amazing channel. I feel so blessed to have found this channel

I have watched these videos over and over then stopped and came back right now at my 7th grade. Pretty cool finding some things froms school ( the triangle meaning the change between two parameters for example)

This content is truly gold! You explained differential equations and solutions to differential equations, without actually going into the depths of calculus! But instead, you made it intuitive. Even more importantly, you used simulations to show that real world examples are not as neatly packaged as the precise equations; there is randomness and chaos.

I fell in love with this channel, I hope you reach 1 million soon

My only complaint is that the background music sounds like my old alarm sound and I’m getting PTSD. Other than that, I think this channel is a hidden gem buried in the depths of boring repetitive content of RU-vid

Hello, Can you share the source code of your simulations? I am interested in knowing your techniques. Ty. PD: Excellent videos. One of the best channels!.

What a nice way to teach people about differential equations, without them realising it! That's some quality content!

Great video as always please keep making more videos

Thank you so much for such a wonderful video

Someone linked one of your videos on reddit, and now I'm in full binge mode. Your presentation reminds me a lot of 3B1B, here's hoping you get a similar subscriber count soon!

Nice videos! I love mathematical biology and it's great to see you tackling this topic this way.

really interesting video, subscribed! :)

Almost at 1million! Great channel

It's really interesting how you got to make qualitative analysis of differential equations *without* the need to introduce any derivative. Kudos for that.

how does this only have 10k views

Will you eventually add into the model the concept of the Death Rate itself changing as the number of creatures changes? Basically like logistic growth?

You are awesome. Definitly going to show some of your videos in my science class :)

Dude please keep up the good work. These videos are extremely impressive for an independent creator. I can't believe you don't have more success yet.

What program do you use to code the simulation? Love the videos btw.

When you showcased the replication rate being equal to the death rate and when it’s greater, I noticed the function graph integrates to the population graph which is so cool, my face lit up when I realized that connection

very stylish video, love it

I just discovered this series and I'm using it to help me create species for my stories more logically

This man is out here teaching calculus. This is one of the greatest channels.

The thumbnail with the blob going up the exponential curve like a rollercoaster is just perfect

Good content. Keep up the good work!

The music in the background is a banger. Love it

I love this so much. Keep making videos, this is a rare treasure of the RU-vid algorithms

this series is really cool

I could watch these for hours I love biology please don’t stop

One of the best channels of youtube

Primer: This is called extinction, it’s over for those creatures Aldabra Rail bird: cha cha real smooth

Just discovered your videos, watched through them all. Commenting to aid the algorithm

I just found this channel, and I find it oddly relaxing.

Ay man try and upload more. this one of the best channels btw

These are superb.

This so interesting yet educational

Really smooth

Just discovered this channel ... totally love it ... love the background music ... but a slight adjustment to the music volume ... just a tad too loud .... but otherwise this is just marvelous!

amazing! thanks

you are probably the smartest RU-vidr ever and you deserve more views

When you say it, it makes so much sense. You show how the different rates of birth death and spontaneous growth levels it self out even when the death in higher, but if the spontaneous rate were to be 0% than you would have to have the birth and death ratio the same or it will loose control. But if the growth is too high obviously like your other video it will start to level its self out but due to different mutations can change population but maintain a ongoing civilisation. Man your smart!!! I would love to see more!!!!

Good work bro

I love this, thank you

Nice job sneaking in some differential equations

This is together with Kurzgesagt how all of RU-vid should look like (I know that there are a lot of very good channels, and not all of them are educational, but I like this kind of videos the most)

0:30 - my favorite sentence in this video.

This shit is QUALITY and super interesting

Nice video!

Great vid!!

I forgot how a function worked but I looked it up and I now understand this a bit better

excellent educational videos. I hope this brilliant content helps you reach your goal.

dude, you need more than 500 k subs... At least a million

Fun Fact: the music is also in 'stable' equlibrium, notice the entire song is in F#, the pitch is going a several notes higher or lower but always comes back to F#.

Thanks!

I hope you reach one million subscribers you deserve it

Wonderful!!