{"id":11768,"date":"2024-12-20T01:07:50","date_gmt":"2024-12-20T06:07:50","guid":{"rendered":"https:\/\/blogs.mathworks.com\/student-lounge\/?p=11768"},"modified":"2025-03-27T16:31:38","modified_gmt":"2025-03-27T20:31:38","slug":"exploring-fractals-and-conways-game-of-life-with-matlab-at-wpi","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/student-lounge\/2024\/12\/20\/exploring-fractals-and-conways-game-of-life-with-matlab-at-wpi\/","title":{"rendered":"Exploring Fractals and Conway’s Game of Life with MATLAB at WPI"},"content":{"rendered":"
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This summer, fifteen high school students from across Massachusetts had the unique opportunity to participate in Explore the World with MATLAB<\/span>, a pre-collegiate Worcester Polytechnic Insitute (WPI) Launch(commuter)<\/a> summer program, led by Dr. Adriana Hera, Principal Application Scientist in the Academic and Research Computing Group. The week-long course was designed to introduce students to MATLAB, focusing specifically on the world of fractals.<\/div>\n
The program kicked off with students getting their first taste of MATLAB. With the help of pre-written code, they learned the basics of fractals and experimented with the patch<\/span><\/a> and plot<\/span><\/a> commands to create and customize colorful houses. The excitement was palpable as students saw their code come to life on the screen.<\/div>\n
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As the week progressed, the challenges became more complex. Students moved from plotting individual flowers to creating intricate fields of flowers, each one unique and vibrant.<\/div>\n
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The midpoint of the week brought a dive into John Conway\u2019s Game of Life, a cellular automaton that simulates the life and death of cells on a grid. John Conway’s Game of Life is a computer simulation that models population changes on a grid of cells, which can be either “alive” or “dead.” Starting with an initial pattern, the simulation follows simple rules: living cells with 2 or 3 neighbors survive, those with fewer than 2 or more than 3 neighbors die, and dead cells with exactly 3 neighbors come to life. By repeatedly applying these rules, you can watch how the patterns evolve over time. This was a turning point for many students, sparking ideas for their own projects.<\/div>\n
One student used MATLAB to model the spread of a disease, comparing scenarios with and without a vaccine. Another explored the competition between two bacterial populations with different growth rates and initial sizes, investigating outcomes like dominance, coexistence, or extinction. The versatility of MATLAB allowed these students to apply their newfound skills to a variety of real-world scenarios.<\/div>\n
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Figure 3: Ruhi S.’s rendeition of the Game of Life for the Number of families who speak languages after passing generations.<\/div>\n
By the fourth day, students were delving deeper into fractals and the rotation of geometric figures, pushing the boundaries of their understanding and creativity. One student, initially inspired by the Game of Life, transitioned to creating a digital rendition of the legendary sword Excalibur, showcasing the flexibility and power of MATLAB.<\/div>\n
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The final day was dedicated to 3D shapes, culminating in a series of presentations where students showcased their projects to peers and parents. The room buzzed with excitement as each student demonstrated their work. I had the privilege of attending these presentations and was impressed by the creativity and technical skill shown. I also shared some MathWorks swag and demonstrated MATLAB\u2019s built-in life<\/span> function (located in the MATLAB \/toolbox\/matlab\/demos\/ directory)<\/span> , a version of Conway\u2019s Game of Life developed by Ned Gulley and one of the co-founders of MathWorks, Cleve Moller.<\/div>\n
Throughout the week, the students not only learned how to approach and solve problems using MATLAB but also explored mathematical concepts, the fundamentals of programming, and the intricate geometry of nature. Their projects spanned diverse applications, from simulating disease spread and bacterial competition to optimizing robot pathfinding and preserving linguistic heritage.<\/div>\n
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One particularly notable project involved using the Game of Life to illustrate the decline of native languages within immigrant families, highlighting the importance of preserving linguistic heritage. Another student simulated interactions between three species, including scenarios with genetic mutations, to study coexistence and population dynamics.<\/div>\n
The students expressed their gratitude for MATLAB documentation, which guided them in coding their projects . One student, Jade V. shared this slide as part of their final presentation.<\/div>\n
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The program not only enhanced their technical skills but also inspired them to think creatively and apply MATLAB to real-world challenges.<\/div>\n
We\u2019re incredibly proud of the students and their accomplishments. Their projects showcased the power of MATLAB in exploring and solving complex problems, and we look forward to seeing how they continue to innovate in the future.<\/div>\n
Stay tuned for more stories from students and educators who are using MATLAB to make a difference in the world!<\/div>\n
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References: https:\/\/blogs.mathworks.com\/cleve\/2012\/09\/03\/game-of-life-part-1-the-rule\/<\/div>\n
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