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<channel>
	<title>yamaanatiq.com</title>
	<link>https://yamaanatiq.com</link>
	<description>yamaanatiq.com</description>
	<pubDate>Wed, 15 Jun 2022 19:15:57 +0000</pubDate>
	<generator>https://yamaanatiq.com</generator>
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	<item>
		<title>About Me</title>
				
		<link>https://yamaanatiq.com/About-Me</link>

		<pubDate>Wed, 19 Sep 2018 04:03:31 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/About-Me</guid>

		<description>Yamaan AtiqLaunch Vehicle/Spacecraft Engineer




	&#60;img width="3004" height="3456" width_o="3004" height_o="3456" data-src="https://freight.cargo.site/t/original/i/1b2676bb52583b52b6540a8264b7cccb5a589c7df0df1786bd6411c2b5214bcc/portraitprofilepic.jpg" data-mid="49207257" border="0"  src="https://freight.cargo.site/w/1000/i/1b2676bb52583b52b6540a8264b7cccb5a589c7df0df1786bd6411c2b5214bcc/portraitprofilepic.jpg" /&#62;
M.S. Aeronautics/Astronautics ‘22
Stanford University
B.S. Mechanical Engineering ‘20
Cornell University
Resume

	My name is Yamaan Atiq. I am currently at SpaceX where I design mission trajectories for the Falcon family of launch vehicles. I am interested in all aspects of navigation, guidance and controls. Previously I spent time at Astra, where I was responsible for GNC algorithm development, controller bringup, and modeling and simulation for the upcoming Rocket and Spacecraft.
I’m passionate about satellites, future launch and commercial flight vehicles. My goal is to help design, analyze, and build the next generation of aircraft, spacecraft, and launch vehicles.&#38;nbsp;
Through past experiences, I have gained experience directly working with next generation vehicles such as Starship, New Glenn, and the A350. Collaborating with great engineers at these companies has helped me develop my technical skills: performing structural analysis and design, and working with technicians to manufacture and integrate flight critical parts. 
	By meeting demanding project schedules, I’ve also learned more about project management and effective communication.

I love working collaboratively, and I’ve developed my management and teamwork skills through leading Cornell Design/Build/Fly’s aerodynamics and controls team. Together, we performed design and analysis to manufacture the wings and empennage of the aircraft. Additionally, I have experience mentoring new members and teaching necessary technical skills such as SolidWorks and MATLAB analysis. Past projects I have led include wing design, analysis, and manufacture, a takeoff analysis design optimization MATLAB program, and fuselage design.
Outside of engineering, I enjoy cooking,&#38;nbsp;spending time outdoors, planespotting, expanding Spotify playlists, and public speaking.
To learn more, please check out my projects and experience.

</description>
		
	</item>
		
		
	<item>
		<title>Experience</title>
				
		<link>https://yamaanatiq.com/Experience-1</link>

		<pubDate>Sat, 24 Aug 2019 22:03:33 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Experience-1</guid>

		<description>&#38;nbsp; Experience</description>
		
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	<item>
		<title>Blue Origin</title>
				
		<link>https://yamaanatiq.com/Blue-Origin</link>

		<pubDate>Wed, 15 Jun 2022 16:35:20 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Blue-Origin</guid>

		<description>
	
Blue Origin
Internship, Summer 2021
	I spent Summer 2021 in Kent, WA supporting R&#38;amp;D of Blue Origin’s orbital launch vehicle New Glenn.

My primary project was investigating a failure mode of the first stage heat exchanger (HEX). In preliminary subscale testing, we observed a flight-critical failure mode and I was responsible for investigating the driving system parameters, so we could ultimately size a system to mitigate the failure. I first performed a literature review which helped identify some critical variables and develop a preliminary MATLAB model. However, the model required validation through experiments so I designed test articles in Creo and developed a test plan. In testing it was challenging to replicate flight like conditions due to the smaller scale and hardware limitations, but I was able to modify my test plan and hardware to represent flight conditions. This allowed me to induce the failure mode and isolate the physical phenomenon causing the failure.

My secondary project involved the HEX control system. I was responsible for developing a real-time system we could use for controls (HITL) testing, which involved writing a wrapper in MATLAB and Simulink to deploy the controller on a Simulink Real-Time machine. I also developed a GUI allowing a test engineer to more easily perform tests and acquire data. This project taught me a lot about understanding flight algorithms, redundancy, and challenges with software and hardware interfaces.
Since these efforts were R&#38;amp;D and New Glenn is largely in its development phase, pictures from these projects cannot be shared. Below is a New Glenn render.




	&#38;nbsp;&#60;img width="2508" height="1406" width_o="2508" height_o="1406" data-src="https://freight.cargo.site/t/original/i/65084f42247c35b8ac92e6b48c5a53371fbcad8777c3756150e8e36a9057590f/NewGlennLaunchRender.png" data-mid="145519804" border="0"  src="https://freight.cargo.site/w/1000/i/65084f42247c35b8ac92e6b48c5a53371fbcad8777c3756150e8e36a9057590f/NewGlennLaunchRender.png" /&#62;
</description>
		
	</item>
		
		
	<item>
		<title>Astranis</title>
				
		<link>https://yamaanatiq.com/Astranis</link>

		<pubDate>Wed, 15 Jun 2022 17:48:13 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Astranis</guid>

		<description>
	
Astranis
Internship, Spring 2021
Full Time, Fall 2021 - Spring 2022
	I joined Astranis as an intern in Spring 2021, eventually converting to a full time employee in Fall 2021, spending about a year working across a variety of interesting spacecraft projects.&#38;nbsp;
A large initial project was developing a center of gravity measuring scale for our spacecraft, to accurately locate to within 5mm. This involved design in Solidworks, analysis in ANSYS, and writing build and operation instructions, as well as testing out the scale to verify accuracy.&#38;nbsp;
Another project was design of a heater system to keep the unpowered spacecraft warm on the Falcon Heavy second stage on its  coast to final&#38;nbsp;Geosynchronous orbit, including a lot of mechanical design and design reviews internally and with our launch provider SpaceX. I also helped to maintain the Interface Control Document (ICD) with our launch provider.
I was responsible for designing our TVAC Payload Test, which involved sizing and procuring RF hardware, working closely with the payload and thermal teams to define requirements and ensure the test setup met space, cost, and assembly constraints.
When I joined back as a full time employee, I owned the mechanical side our Gyroscope system, working closely with the GNC and Avionics teams to ensure my hardware design met sensing, thermal, and assembly requirements. I also worked closely with technicians to ensure the system could be easily and repeatably built, where I relearned an important lesson about always prioritizing technician feedback on a design. This also led to co-owning development of a section of the spacecraft factory, which would be used for mass-building electronics enclosures. Again, it was critical to work closely with technicians and Assembly, Integration and Test engineers to ensure the factory met their build needs.
My final main project revolved around design of our smaller Deployable Splashplate Antenna. I was responsible for mechanical design and packaging of the deployment mechanisms and composite structures. The pointing requirements for this system were very tight, and so it was important to work closely with the Antenna and GNC teams to ensure my design would meet our pointing budget. This involved a mix of studying possible low frequency (launch) and high frequency (thermal) biases that would cause mispointing, and developing a repeatable procedure for aligning the antenna when the system was build. Finally, I characterized these shifts using a mix of lasertracker data and analyzing our models for our GNC team to use in Monte Carlo simulations, so we could conclude our design would meet antenna requirements.
Since these efforts were R&#38;amp;D and Astranis spacecraft are largely in their development phase, below are some public pictures from testing and a recent render.




	&#38;nbsp;&#60;img width="1682" height="1078" width_o="1682" height_o="1078" data-src="https://freight.cargo.site/t/original/i/96c6a5ce6f46d39336716b860a6a1b538da98e59f413ff09dd6018fcb34a2084/106985353-1638851321269-astranis_peru_satellite_3.jpeg" data-mid="145522904" border="0"  src="https://freight.cargo.site/w/1000/i/96c6a5ce6f46d39336716b860a6a1b538da98e59f413ff09dd6018fcb34a2084/106985353-1638851321269-astranis_peru_satellite_3.jpeg" /&#62;
&#60;img width="2560" height="1920" width_o="2560" height_o="1920" data-src="https://freight.cargo.site/t/original/i/95b27e741e7dfb241a94bbc96168c9ede44bb00deb51529a018d29b75a17e08f/Astranis-employee-with-Arcturus-MicroGEO-satellite-inside-TVAC-test-chamber-1-scaled.jpeg" data-mid="145522905" border="0"  src="https://freight.cargo.site/w/1000/i/95b27e741e7dfb241a94bbc96168c9ede44bb00deb51529a018d29b75a17e08f/Astranis-employee-with-Arcturus-MicroGEO-satellite-inside-TVAC-test-chamber-1-scaled.jpeg" /&#62;

</description>
		
	</item>
		
		
	<item>
		<title>SpaceX</title>
				
		<link>https://yamaanatiq.com/SpaceX</link>

		<pubDate>Wed, 19 Sep 2018 04:03:35 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/SpaceX</guid>

		<description>
	
SpaceX
Internship, Summer 2019
	I worked in Hawthorne, CA designing, analyzing, and building structures for SpaceX’s development Mars vehicle Starship.&#38;nbsp;
My main project was bringing Starship’s access door arm mechanism to life. I designed the arm in NX and used ANSYS to iterate the design. Ultimately, the arm weighed 60% less than the door arm used on Starhopper. I gained more experience in mechanical design and welded subassemblies, as well as GD&#38;amp;T standards and producing engineering drawings.

I also developed several structural test fixtures and procedures. These provided design allowables for stiffeners and welds used on Starship, and qualification of secondary structures.&#38;nbsp;

In the later part of the summer, I worked to keep the build of Starship prototypes in Cocoa, FL and Boca Chica, TX on schedule. I planned and executed integration operations for the door stiffeners on the vehicle in Florida, designing necessary tools and jigs to ensure we could progress quickly. 
Below are some public pictures from online fan forums showing the structures on the vehicles in Boca Chica and Cocoa.




	&#38;nbsp;
&#60;img width="1920" height="1440" width_o="1920" height_o="1440" data-src="https://freight.cargo.site/t/original/i/060a1b189f9aa60a4e17672e744e14e9014d32252b4dbad1876101a6aa129972/cocoadoor.jpeg" data-mid="49034492" border="0"  src="https://freight.cargo.site/w/1000/i/060a1b189f9aa60a4e17672e744e14e9014d32252b4dbad1876101a6aa129972/cocoadoor.jpeg" /&#62;
&#60;img width="5472" height="3648" width_o="5472" height_o="3648" data-src="https://freight.cargo.site/t/original/i/04e97e4e99a30d10b8e2770319dcf4eac4e89b75a877ba1b2ce0191950bbb732/tankdoors.JPG" data-mid="49034496" border="0" data-scale="100" src="https://freight.cargo.site/w/1000/i/04e97e4e99a30d10b8e2770319dcf4eac4e89b75a877ba1b2ce0191950bbb732/tankdoors.JPG" /&#62;
&#60;img width="1200" height="800" width_o="1200" height_o="800" data-src="https://freight.cargo.site/t/original/i/3676b0a9d08b3d7dc189efa2fd7f846efd09fed727368c5da6face2b017cb038/elon-musk-spacex-spaceship-1200x800.jpg" data-mid="51699606" border="0"  src="https://freight.cargo.site/w/1000/i/3676b0a9d08b3d7dc189efa2fd7f846efd09fed727368c5da6face2b017cb038/elon-musk-spacex-spaceship-1200x800.jpg" /&#62;
&#60;img width="1280" height="1920" width_o="1280" height_o="1920" data-src="https://freight.cargo.site/t/original/i/7ff5596052d2da99c19a69065cfa61c868885f8d46359747e20c3dec07f64c4e/bocadoor.jpeg" data-mid="49034493" border="0"  src="https://freight.cargo.site/w/1000/i/7ff5596052d2da99c19a69065cfa61c868885f8d46359747e20c3dec07f64c4e/bocadoor.jpeg" /&#62;
&#60;img width="2048" height="1366" width_o="2048" height_o="1366" data-src="https://freight.cargo.site/t/original/i/a81ce1c17d47334e2a09cbacd86177c78fecc9b422d2f0bef635ce02b6396d08/thruststructure.jpeg" data-mid="49034495" border="0"  src="https://freight.cargo.site/w/1000/i/a81ce1c17d47334e2a09cbacd86177c78fecc9b422d2f0bef635ce02b6396d08/thruststructure.jpeg" /&#62;
&#60;img width="682" height="1024" width_o="682" height_o="1024" data-src="https://freight.cargo.site/t/original/i/681158f92168b8e88b5ca95bd73d05fe529d0101e92113ff78b40c99e3cb5d2f/EFW5Tx2U0AAzU35.jpeg" data-mid="51527664" border="0"  src="https://freight.cargo.site/w/682/i/681158f92168b8e88b5ca95bd73d05fe529d0101e92113ff78b40c99e3cb5d2f/EFW5Tx2U0AAzU35.jpeg" /&#62;

</description>
		
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	<item>
		<title>Northrop Grumman Innovation Systems</title>
				
		<link>https://yamaanatiq.com/Northrop-Grumman-Innovation-Systems</link>

		<pubDate>Wed, 19 Sep 2018 04:03:35 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Northrop-Grumman-Innovation-Systems</guid>

		<description>
	Northrop Grumman Innovation Systems 
(formerly Orbital ATK)Internship, Summer 2018
	I spent Summer 2018 in Clearfield, UT as an aerospace structures intern at Northrop Grumman Innovation Systems. My work focused on improving composite T-stringer and Z-frame manufacturing for the A350 XWB and A400M aircraft.&#38;nbsp;
&#60;img width="500" height="333" width_o="500" height_o="333" data-src="https://freight.cargo.site/t/original/i/100527a9848754cd2616406bb5074520ab043f88451daf7b9aa275c49e1d05ad/cw_camx_15_orbital_atk_1_500.jpg" data-mid="48897816" border="0" data-scale="100" alt="A350 Linear Stringer Cleanroom " data-caption="A350 Linear Stringer Cleanroom " src="https://freight.cargo.site/w/500/i/100527a9848754cd2616406bb5074520ab043f88451daf7b9aa275c49e1d05ad/cw_camx_15_orbital_atk_1_500.jpg" /&#62;

I performed trade studies to evaluate and improve tooling designs, resulting in significant cost savings by reducing the scrap rate. I also developed improvements to stringer manufacturing processes and optimized machines to save hundreds of labor-hours in fabrication time.

&#60;img width="4032" height="1960" width_o="4032" height_o="1960" data-src="https://freight.cargo.site/t/original/i/36ea86a19e54a9f82814b5901f08eecdfa37aa8dcd7473fa8f9ea64d959ba5ad/autoclave.jpg" data-mid="48899025" border="0" data-scale="100" alt="Autoclave" data-caption="Autoclave" src="https://freight.cargo.site/w/1000/i/36ea86a19e54a9f82814b5901f08eecdfa37aa8dcd7473fa8f9ea64d959ba5ad/autoclave.jpg" /&#62;
</description>
		
	</item>
		
		
	<item>
		<title>Projects</title>
				
		<link>https://yamaanatiq.com/Projects</link>

		<pubDate>Sat, 24 Aug 2019 22:05:00 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Projects</guid>

		<description>&#38;nbsp; &#38;nbsp; Projects</description>
		
	</item>
		
		
	<item>
		<title>Lasercut Stained Maps</title>
				
		<link>https://yamaanatiq.com/Lasercut-Stained-Maps</link>

		<pubDate>Wed, 15 Jun 2022 19:15:57 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Lasercut-Stained-Maps</guid>

		<description>
	Lasercut Stained Maps
Fall 2021
	I’ve always found lasercut topographical maps to be extremely fascinating, yet simple pieces of art, and so in Fall 2021 I decided to go about making my own. The process is quite simple, only requiring topographical data (the hard part), a laser cutter (the less hard part), and wood (the easy part).&#38;nbsp;
I start by finding topobathy (topographical and bathymetry) data which is used to generate layer heights. Websites like ArcGIS provide this at a cost, but depending on the city or region, if common enough, the following websites provide good alternatives:
https://topotools.cr.usgs.gov/topobathy_viewer/https://download.gebco.net/

With the raw elevation data, I use QGIS which is a free, open source, map processor to define my discrete layer heights. The layer heights are not uniform, since this generates a more aesthetically pleasing piece. I can then export that data as contour lines and layers to a vector image processor (I use Inkscape for Mac) to generate dxfs for laser cutting. Finally, I use nesting software (DeepNest) to create efficiently spaced sheets for lasercutting. Here is an example from a UK Map.
&#60;img width="312" height="1290" width_o="312" height_o="1290" data-src="https://freight.cargo.site/t/original/i/be926d098ccd36cbd7f3d810bd3fb1483195f01fb7904c7a50b6b2efb76770ef/Screen-Shot-2022-06-15-at-12.24.31-PM.png" data-mid="145531460" border="0" data-scale="35" src="https://freight.cargo.site/w/312/i/be926d098ccd36cbd7f3d810bd3fb1483195f01fb7904c7a50b6b2efb76770ef/Screen-Shot-2022-06-15-at-12.24.31-PM.png" /&#62;
Once the dxf is ready, I lasercut approximately 1/8” thick pieces of Baltic Birch plywood, and stain the correct bottom layers. Usually, I will also lasercut a rectangle of the correct size as the base. I typically aim for 8 - 10 wood layers, resulting in a map about 1.5-2” thick. This is good for most frames.
&#60;img width="3024" height="4032" width_o="3024" height_o="4032" data-src="https://freight.cargo.site/t/original/i/8a4872c4e1c395e1029aa1d6407c685e88efa893ed5353f3b9ec5ed3d7d51b27/20211025_225422.jpg" data-mid="145531183" border="0"  src="https://freight.cargo.site/w/1000/i/8a4872c4e1c395e1029aa1d6407c685e88efa893ed5353f3b9ec5ed3d7d51b27/20211025_225422.jpg" /&#62;
I stain the bottom layers using dark navy blue wood stain, and then use a lacquer spray to protect the wood from moisture or other damage. Finally, I use wood glue and clamp together for about a day, making sure to scrape excess.

&#60;img width="4032" height="3024" width_o="4032" height_o="3024" data-src="https://freight.cargo.site/t/original/i/6f17a60146e6b81b82575d76a7a3e9b742f1fadf1a7165277796762da270afa7/20211026_211713.jpg" data-mid="145531171" border="0"  src="https://freight.cargo.site/w/1000/i/6f17a60146e6b81b82575d76a7a3e9b742f1fadf1a7165277796762da270afa7/20211026_211713.jpg" /&#62;
&#60;img width="4032" height="3024" width_o="4032" height_o="3024" data-src="https://freight.cargo.site/t/original/i/2af5a269c1831c783982c7365f3e4436a141bcfc7a014d954963070ead4e0a4a/20211026_211644.jpg" data-mid="145531470" border="0"  src="https://freight.cargo.site/w/1000/i/2af5a269c1831c783982c7365f3e4436a141bcfc7a014d954963070ead4e0a4a/20211026_211644.jpg" /&#62;
The last step is optional, but for me I like to frame my pieces. Framing can be quite expensive, especially for custom dimension pieces like these. I found&#38;nbsp;americanframe.com and similar sites offer affordable frames custom dimensioned for pieces. Once framed, the piece is complete!

&#60;img width="4032" height="3024" width_o="4032" height_o="3024" data-src="https://freight.cargo.site/t/original/i/4e81d1fe767d6fc8cc5602df2315c4b2d24c8904f2293e245185e3a6dd12c289/20211103_182335.jpg" data-mid="145531178" border="0"  src="https://freight.cargo.site/w/1000/i/4e81d1fe767d6fc8cc5602df2315c4b2d24c8904f2293e245185e3a6dd12c289/20211103_182335.jpg" /&#62;

</description>
		
	</item>
		
		
	<item>
		<title>Custom CFD Solver</title>
				
		<link>https://yamaanatiq.com/Custom-CFD-Solver</link>

		<pubDate>Wed, 23 Sep 2020 02:21:58 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Custom-CFD-Solver</guid>

		<description>
	Custom CFD Solver
Summer 2020
	During Spring 2020 I took MAE 6230, an introductory CFD class that allowed me to write my first CFD solver in MATLAB. For my final class project, I implemented a solver to solve the Navier-Stokes equations around a blunt body suspended in a flow. The initial solver could only solve low Reynolds number flows, but I found the project quite interesting as a baseline for more complicated flow phenomena, which I took on as a personal project over Summer 2020.
For spatial discretization, I used a second order finite volume method on a staggered variable mesh to eliminate the checkerboarding effect. For temporal discretization I used the fractional step method (Kim &#38;amp; Moin 1985). This is an explicit second order Adams-Bashform discretization of convection combined with a second order Crank-Nicolson discretization of viscosity. I also implemented a third order QUICK scheme to solve the scalar transport equations necessary for the various flows (whether dyes or flames). To solve the linear pressure system, I implemented a Krylov-based solver, using the conjugate gradient method.
The first flow shows Kármán vortex streets being shed in a square cylinder’s wake at Re = 400.


Following on from the initial solver,&#38;nbsp; I implemented some other types of flows. One is a Large Eddy Simulation (LES) solver. The LES models turbulence so the simulation can be run above Re = 10000. Vortex shedding is rougher and more shaky as Reynolds number is increased. The Smagorinsky constant coefficient model is used, and variables are implicitly filtered by the mesh.

The next solver uses the same model, but implements a particle in a jet. These particles are inserted randomly at the inlet and follow the fluid. I integrated their trajectories using a 4th order Runge-Kutta method.

Finally, there I modeled premixed combustion over the same blunt body, igniting the region behind the body to analyze the development of the flame with a chosen holder. This design could be changed to evaluate the effectiveness at various Reynolds numbers. Similar discretization methods are involved for solving flame scalar equations, such as combustion and temperature. Below is the result for Re = 1000.
&#60;img width="1120" height="840" width_o="1120" height_o="840" data-src="https://freight.cargo.site/t/original/i/4a7123ad9a10988db535940b1784085e0c688419eec78eace7384ccd24f5d413/CombustionSimulationRe1000_customcolor.gif" data-mid="83513595" border="0"  src="https://freight.cargo.site/w/1000/i/4a7123ad9a10988db535940b1784085e0c688419eec78eace7384ccd24f5d413/CombustionSimulationRe1000_customcolor.gif" /&#62;
The full codes can be found on GitHub.
</description>
		
	</item>
		
		
	<item>
		<title>Mandelbrot &#38; Julia Sets</title>
				
		<link>https://yamaanatiq.com/Mandelbrot-Julia-Sets</link>

		<pubDate>Wed, 23 Dec 2020 13:47:44 +0000</pubDate>

		<dc:creator>yamaanatiq.com</dc:creator>

		<guid isPermaLink="true">https://yamaanatiq.com/Mandelbrot-Julia-Sets</guid>

		<description>
	Mandelbrot &#38;amp; Julia Sets
Summer 2020
	I’ve always been amazed by fractals. They look infinitely complex, yet are actually simpler to represent using mathematics than you might expect.&#38;nbsp;
&#60;img width="3057" height="2483" width_o="3057" height_o="2483" data-src="https://freight.cargo.site/t/original/i/d112b4b951a81a3b2f47a2baf006b412e7c6a869031785c7dc75518944173b31/Romanesco.jpg" data-mid="92948025" border="0" alt="Romanesco Fractal" data-caption="Romanesco Fractal" src="https://freight.cargo.site/w/1000/i/d112b4b951a81a3b2f47a2baf006b412e7c6a869031785c7dc75518944173b31/Romanesco.jpg" /&#62;
This picture of romanesco broccoli is one of my favourites.

The most astounding part for me is that they’re found all over nature - shells, leaves, coastlines. I think fractals are some of our clearest evidence that mathematics is the language of the universe. I wanted to experiment with generating my own, so wrote a script to visualise the Mandelbrot and Julia sets.The Mandelbrot and Julia sets are defined pretty generally mathematically, but here I just describee their visualization.To start, we look at a region of interest in the complex plane (for example the real and imaginary axes going from -5 to 5), and run each complex “point” z in the region (in reality there are infinite points, so we just take each pixel) through an expression. For Julia sets, this expression follows zk+1&#38;nbsp;= zkn + c, where n and c can be varied to generate many different patterns. Each point is iterated through the expression and if the value z exceeds a given magnitude R in a finite number of iterations, the iteration is recorded. Otherwise, the point z is said not to diverge and this is noted. A corresponding color map graphically represents the number of iterations for each pixel in the image, and if the point does not diverge it is left black.
As an example, set n to 2 and c = 0.8 + 0.156i. With a convergence radius R set to 2, you produce the first picture below.
The Mandelbrot set is similarly generated, except each point in the region of interest is the fixed c in the above expression, n is always set to 2, R is set to 2, and z0 = 0 for each point iterated.&#38;nbsp;
Below are a sample of some Julia set pictures generated using different constants and powers in the iterations.
&#60;img width="903" height="501" width_o="903" height_o="501" data-src="https://freight.cargo.site/t/original/i/6f083a680a205147ef5c5c4b5be2992a8a4cd75d6d7d62ebf603ea0f104f8f49/Julia_n2_R2_cx-0.8_cy0.156.png" data-mid="92946157" border="0"  src="https://freight.cargo.site/w/903/i/6f083a680a205147ef5c5c4b5be2992a8a4cd75d6d7d62ebf603ea0f104f8f49/Julia_n2_R2_cx-0.8_cy0.156.png" /&#62;
&#60;img width="902" height="504" width_o="902" height_o="504" data-src="https://freight.cargo.site/t/original/i/7215a592c57c62c7b1cb367eee890a028f505dfabc4150484638f6be345bd6d2/Julia_n2_R2_cx-0.123_cy0.745.png" data-mid="92946159" border="0"  src="https://freight.cargo.site/w/902/i/7215a592c57c62c7b1cb367eee890a028f505dfabc4150484638f6be345bd6d2/Julia_n2_R2_cx-0.123_cy0.745.png" /&#62;



 


&#60;img width="903" height="504" width_o="903" height_o="504" data-src="https://freight.cargo.site/t/original/i/872186296d626f78c20d3db89ffba5e2146c48b9cf829f7a025e8fefc7f8b6f1/Julia_n2_R2_cx0_cy0.png" data-mid="92946160" border="0"  src="https://freight.cargo.site/w/903/i/872186296d626f78c20d3db89ffba5e2146c48b9cf829f7a025e8fefc7f8b6f1/Julia_n2_R2_cx0_cy0.png" /&#62;&#60;img width="903" height="505" width_o="903" height_o="505" data-src="https://freight.cargo.site/t/original/i/b3ebc380ec367b7b09e05955c1effbfe2adebfa91aeb270cb0c237fdfc0f7fea/Julia_n5_R2_cx-0.8_cy0.156.png" data-mid="92946161" border="0"  src="https://freight.cargo.site/w/903/i/b3ebc380ec367b7b09e05955c1effbfe2adebfa91aeb270cb0c237fdfc0f7fea/Julia_n5_R2_cx-0.8_cy0.156.png" /&#62;&#60;img width="903" height="505" width_o="903" height_o="505" data-src="https://freight.cargo.site/t/original/i/b526a886a191421efb9bce42819714f3f56fe0fea7cfe03e06360efa3d7bb91a/Julia_n10_R2_cx-0.8_cy0.156.png" data-mid="92946162" border="0"  src="https://freight.cargo.site/w/903/i/b526a886a191421efb9bce42819714f3f56fe0fea7cfe03e06360efa3d7bb91a/Julia_n10_R2_cx-0.8_cy0.156.png" /&#62;&#60;img width="902" height="509" width_o="902" height_o="509" data-src="https://freight.cargo.site/t/original/i/2caaf8f8fe1c98acd98afea5ef06cffd18515343d98e85d97651824c51f10627/Julia_n6_R2_cx-0.8_cy0.156.png" data-mid="92946163" border="0"  src="https://freight.cargo.site/w/902/i/2caaf8f8fe1c98acd98afea5ef06cffd18515343d98e85d97651824c51f10627/Julia_n6_R2_cx-0.8_cy0.156.png" /&#62;
&#60;img width="903" height="505" width_o="903" height_o="505" data-src="https://freight.cargo.site/t/original/i/69bb9b9a90eae38e8b636e5395f2a4cc9c8863af23cdebbdd89ebbe462f64be0/Julia_n2_R2_cx-0.4_cy0.6.png" data-mid="92946158" border="0"  src="https://freight.cargo.site/w/903/i/69bb9b9a90eae38e8b636e5395f2a4cc9c8863af23cdebbdd89ebbe462f64be0/Julia_n2_R2_cx-0.4_cy0.6.png" /&#62;
The full codes can be found on GitHub.
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