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Abstract: The Boltzmann distribution is one of the key equations of thermal physics andis widely used in machine learning as well. Here I derive a Boltzmanndistribution in a simple pedagogical example using only tools from a first-yearprobability course. The example is called 'coconuts and islanders' and wastaught to me by my father, Shoucheng Zhang (1963 - 2018), to whom these notesare dedicated. By focusing on this simple story, which can be easily simulatedon a computer, I aim to provide a more accessible and intuitive presentation ofthe Boltzmann distribution. Yet I hope this exposition also inspires deepthinking about statistical physics. For instance, I show that the coconuts andislanders story illuminates a connection between the 'fundamental assumption ofstatistical mechanics'---all microstates are equally probable---and thestatistical property of detailed balance.

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From: Brian Zhang [view email]
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Sun, 7 Apr 2019 22:39:00 UTC (51 KB)
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Team:Friedemann Allmenröder, Jonas Tyroller, Paul Schnepf
ISLANDERS
Engine: Unity 3D
Platform: PC
Release Date: 04.04.2019
Download:https://store.steampowered.com/app/1046030/ISLANDERS
Islanders is a minimalist strategy game about building beautiful cities on colorful islands. Explore an infinite number of ever-changing new lands, expand your settlements from sprawling villages to vast cities and enjoy the relaxing atmosphere. The core-mechanic is deceptively simple: You get points by placing buildings, based on which other structures surround them. However, this quickly gets more challenging and interesting as you unlock additional buildings and travel to new islands with ever-changing terrain and building conditions.
ISLANDERS
We created Islanders in 4 months as part of the third year in our Game Design program at HTW Berlin. After some initial days of prototyping and research on a great variety of topics, we fell in love with the idea of a casual city building game that still offers enough depth to be played hours on end. At the beginning it was quite a challenge to find mechanics that provided complex enough gameplay without sacrificing the game's simplicity. It took us another few weeks of different prototypes until we ended up with the proximity mechanic that lies at the heart of Islanders. From there on we shaped everything else around this one mechanic, trying to keep the experience as simple and streamlined as possible.

Islanders Free Download

We are super grateful for the endless stream feedback we received from our professors and all people that tested the game. At the end of the 4 months of development time at uni we took another 2 months to polish the game, prepare its release and do some marketing. Eventually we released Islanders on the 4th of April 2019 on Steam.
Besides some gameplay programming I was responsible for UX design and the user interface in Islanders. While designing the user experience I focussed on two things: Embracing pleasure in the core gameloop and optimizing the experience of new players. The mechanics of Islanders are so simple that you basically just repeat one action over and over again – placing buildings onto the Island. Obviously that action should feel as good as possible.

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Thus I not only spent a ridiculous amount of time to let the buildings wiggle juuust right when built, but also made sure that players recieve non-stop feedback for their actions. While dragging a building for example, the game constantly projects the predicted score into the game world, highlighting which other buildings contribute to it. Once a building is placed the flow of coins indicates what the points are rewarded for. This is not only very satisfying, but also makes it easy to understand for players what effect their actions had.

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Minimalism is something we tried to apply wherever possible. As a result of this approach not only the gameplay itself but also the user interface is clean and easy to understand. The UI only displays what is relevant for the current game state. When you start the game for the first time, you learn the basics in a brief and seamlessly integrated tutorial. The rest is designed in a way that is self explanatory and unbreakable, so it's actually fun to explore the game's depths on your own. All UI elements are non-intrusive. Even on entering menus, the island you're playing on never disappears from the screen, providing an undisrupted play session.