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FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
ABOUT US – FRACTAL FOUNDATION The Fractal Foundation was formed in 2003, as an outgrowth of the Albuquerque based “Chaos Club”. Since then, we have taught fractals to over 69,000 children and 55,000 adults. Based in Albuquerque, most of our activities have thus far taken place in NewMexico, but
FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
ONLINE FRACTAL COURSE Online Fractal Course. We are proud to announce the launching of an online fractal course. It has been developed by the Fractal Foundation in collaboration with UNM under a grant from the NM Public Education Department. While the course is primarily aimed at high school students, anyone may browse the material and do the exercises andactivities.
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION ONLINE COURSE Start with the 0 order triangle in the figure above. The next iteration, order 1, is made up of 3 smaller triangles. And order 2 is made up of 9 triangles. So each iteration of the fractal has 3 times as many triangles, and N=3. Next we need to figure out the scalingfactor, r.
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Sierpinski Triangle. Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below. Just by repeating this simple process, a fascinating pattern is built up.It’s lots of
FRACTAL TRIANGLES
Fractal Triangles Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, allrights reserved 1
FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
ABOUT US – FRACTAL FOUNDATION The Fractal Foundation was formed in 2003, as an outgrowth of the Albuquerque based “Chaos Club”. Since then, we have taught fractals to over 69,000 children and 55,000 adults. Based in Albuquerque, most of our activities have thus far taken place in NewMexico, but
FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
ONLINE FRACTAL COURSE Online Fractal Course. We are proud to announce the launching of an online fractal course. It has been developed by the Fractal Foundation in collaboration with UNM under a grant from the NM Public Education Department. While the course is primarily aimed at high school students, anyone may browse the material and do the exercises andactivities.
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION ONLINE COURSE Start with the 0 order triangle in the figure above. The next iteration, order 1, is made up of 3 smaller triangles. And order 2 is made up of 9 triangles. So each iteration of the fractal has 3 times as many triangles, and N=3. Next we need to figure out the scalingfactor, r.
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Sierpinski Triangle. Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below. Just by repeating this simple process, a fascinating pattern is built up.It’s lots of
FRACTAL TRIANGLES
Fractal Triangles Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, allrights reserved 1
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
STORE – FRACTAL FOUNDATION Click to Visit our Store Now! Wearing fractals is FUN!!! And by purchasing fractal merchandise, you are supporting science, math and art education in New Mexico.LEARN TO CODE!
Learn to Code! Creating fractal software is a fun and easy introduction to coding. Because fractals are made by repeating simple processes, it is actually quite easy to create simple programs that make dazzling fractal patterns. Julia and Maya – 2 interns at the FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. XAOS – FRACTAL FOUNDATION Use free software to explore fractals and create beautiful art. XaoS (https://fractalfoundation.org/resources/fractal-software/) is free software that allows us to FRACTAL FOUNDATION ONLINE COURSE Now we will explore the formation of spirals in more detail, and discover some more interesting and useful facts about Fibonacci Numbers. We will be examining the concept of periodicity, which we'll also learn about in the Mandelbrot Set, but which is also important in a large number of natural systems.. Perhaps the simplest, most elegant example of a spiral in nature is a seashell. FRACTAL FOUNDATION ONLINE COURSE Another naturally occurring fractal pattern is a lightning bolt. As Benoit Mandelbrot noted in the opening quotation, lightning does not travel in straight lines. FRACTAL FOUNDATION ONLINE COURSE Play with the fractal above for a while. Explore the details on the edge. You can find (literally) countless examples of Self-Similar patterns within the Mandelbrot Set. But interestingly, unlike the simple IFS fractals from the previous chapter, which show the same kind of detail everywhere, at all scales, the Mandelbrot Set is NOT perfectly self-similar.XAOS INSTRUCTIONS
XaoS Instructions. First, Download the correct version of the program for your computer. Installation (PC): Unzip the folder “XaoS” onto the desktop. Within this folder, there is a directory “bin”. Use the “XaoS” icon inside to run the program. Macintosh: Save “XaoS-3.2.2-MacOSX.dmg to the desktop and click on it to install.Run
FRACTAL FOUNDATION ONLINE COURSE The Golden Ratio. The Fibonacci Sequence appears in many seemingly unrelated areas. In this section we'll see how the Fibonacci Sequence generates the Golden Ratio, a relationship so special it has even been called "the Divine Proportion."FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. FRACTAL FOUNDATION ONLINE COURSE Start with the 0 order triangle in the figure above. The next iteration, order 1, is made up of 3 smaller triangles. And order 2 is made up of 9 triangles. So each iteration of the fractal has 3 times as many triangles, and N=3. Next we need to figure out the scalingfactor, r.
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Sierpinski Triangle. Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below. Just by repeating this simple process, a fascinating pattern is built up.It’s lots of
FRACTAL FOUNDATION ONLINE COURSE Questions: What is the SA:V ratio for our lungs? Assume the lungs have a Surface Area of 100 m 2 and a Volume of 5 liters. Give your answer first in m 2 /L Now, to make this measurement more useful, we need to convert liters to cubic meters.FRACTAL TRIANGLES
Fractal Triangles Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, allrights reserved 1
FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. FRACTAL FOUNDATION ONLINE COURSE Start with the 0 order triangle in the figure above. The next iteration, order 1, is made up of 3 smaller triangles. And order 2 is made up of 9 triangles. So each iteration of the fractal has 3 times as many triangles, and N=3. Next we need to figure out the scalingfactor, r.
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Sierpinski Triangle. Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below. Just by repeating this simple process, a fascinating pattern is built up.It’s lots of
FRACTAL FOUNDATION ONLINE COURSE Questions: What is the SA:V ratio for our lungs? Assume the lungs have a Surface Area of 100 m 2 and a Volume of 5 liters. Give your answer first in m 2 /L Now, to make this measurement more useful, we need to convert liters to cubic meters.FRACTAL TRIANGLES
Fractal Triangles Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, allrights reserved 1
ABOUT US – FRACTAL FOUNDATION The Fractal Foundation was formed in 2003, as an outgrowth of the Albuquerque based “Chaos Club”. Since then, we have taught fractals to over 69,000 children and 55,000 adults. Based in Albuquerque, most of our activities have thus far taken place in NewMexico, but
ONLINE FRACTAL COURSE Online Fractal Course. We are proud to announce the launching of an online fractal course. It has been developed by the Fractal Foundation in collaboration with UNM under a grant from the NM Public Education Department. While the course is primarily aimed at high school students, anyone may browse the material and do the exercises andactivities.
FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission.FRACTAL BALLOONS
Both balloons will be appearing at schools, community events and balloon festivals everywhere, inspiring audiences with the beauty of math and science. To inquire about creating your own fractal art balloon with us, or to invite Infinitude or Fibonacci to your event, FRACTAL FOUNDATION ONLINE COURSE Starting with a simple triangle, the first step, shown in the figure, is to remove the middle triangle. This leaves behind 3 black triangles surrounding a central white triangle (iteration 1).XAOS INSTRUCTIONS
XaoS Instructions. First, Download the correct version of the program for your computer. Installation (PC): Unzip the folder “XaoS” onto the desktop. Within this folder, there is a directory “bin”. Use the “XaoS” icon inside to run the program. Macintosh: Save “XaoS-3.2.2-MacOSX.dmg to the desktop and click on it to install.Run
FRACTAL FOUNDATION ONLINE COURSE Again, the slope of the line equals the dimension, and it is defined as the amount of change along the Y-axis, divided by the amount of change along the X-axis. FRACTAL FOUNDATION ONLINE COURSE Questions: Start with 100 fish in a pond (P 0).Assume a fertility factor of .5, and that the carrying capacity of the pond is 200. Use the Verhulst equation to calculate the number of fish at the next generation, P 1: Calculate the number at the second generation, P 2: Hint: your answer should be larger than the carrying capacity, which is unsustainable. FRACTAL FOUNDATION ONLINE COURSE The answer is that the network of tributaries collects water from a huge surface area of land and funnels it into the river. Even though it may not have rained recently where you happen to be watching the river, somewhere upstream it probably rained on some of the tributaries, possibly hundreds or sometimes even thousands ofkilometers away.
FRACTAL FOUNDATION ONLINE COURSE The Golden Ratio. The Fibonacci Sequence appears in many seemingly unrelated areas. In this section we'll see how the Fibonacci Sequence generates the Golden Ratio, a relationship so special it has even been called "the Divine Proportion."FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. FRACTAL FOUNDATION ONLINE COURSE Start with the 0 order triangle in the figure above. The next iteration, order 1, is made up of 3 smaller triangles. And order 2 is made up of 9 triangles. So each iteration of the fractal has 3 times as many triangles, and N=3. Next we need to figure out the scalingfactor, r.
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Sierpinski Triangle. Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below. Just by repeating this simple process, a fascinating pattern is built up.It’s lots of
FRACTAL FOUNDATION ONLINE COURSE Questions: What is the SA:V ratio for our lungs? Assume the lungs have a Surface Area of 100 m 2 and a Volume of 5 liters. Give your answer first in m 2 /L Now, to make this measurement more useful, we need to convert liters to cubic meters.FRACTAL TRIANGLES
Fractal Triangles Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, allrights reserved 1
FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. FRACTAL FOUNDATION ONLINE COURSE Start with the 0 order triangle in the figure above. The next iteration, order 1, is made up of 3 smaller triangles. And order 2 is made up of 9 triangles. So each iteration of the fractal has 3 times as many triangles, and N=3. Next we need to figure out the scalingfactor, r.
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Sierpinski Triangle. Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below. Just by repeating this simple process, a fascinating pattern is built up.It’s lots of
FRACTAL FOUNDATION ONLINE COURSE Questions: What is the SA:V ratio for our lungs? Assume the lungs have a Surface Area of 100 m 2 and a Volume of 5 liters. Give your answer first in m 2 /L Now, to make this measurement more useful, we need to convert liters to cubic meters.FRACTAL TRIANGLES
Fractal Triangles Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, allrights reserved 1
ABOUT US – FRACTAL FOUNDATION The Fractal Foundation was formed in 2003, as an outgrowth of the Albuquerque based “Chaos Club”. Since then, we have taught fractals to over 69,000 children and 55,000 adults. Based in Albuquerque, most of our activities have thus far taken place in NewMexico, but
FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission.FRACTAL BALLOONS
Both balloons will be appearing at schools, community events and balloon festivals everywhere, inspiring audiences with the beauty of math and science. To inquire about creating your own fractal art balloon with us, or to invite Infinitude or Fibonacci to your event, FRACTAL FOUNDATION ONLINE COURSE Starting with a simple triangle, the first step, shown in the figure, is to remove the middle triangle. This leaves behind 3 black triangles surrounding a central white triangle (iteration 1). FRACTAL FOUNDATION FRACTIVITIES Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, all rights reserved Fractal Foundation Fractivities FRACTAL FOUNDATION ONLINE COURSE Again, the slope of the line equals the dimension, and it is defined as the amount of change along the Y-axis, divided by the amount of change along the X-axis. FRACTAL FOUNDATION ONLINE COURSE Questions: Start with 100 fish in a pond (P 0).Assume a fertility factor of .5, and that the carrying capacity of the pond is 200. Use the Verhulst equation to calculate the number of fish at the next generation, P 1: Calculate the number at the second generation, P 2: Hint: your answer should be larger than the carrying capacity, which is unsustainable. FRACTAL FOUNDATION ONLINE COURSE The answer is that the network of tributaries collects water from a huge surface area of land and funnels it into the river. Even though it may not have rained recently where you happen to be watching the river, somewhere upstream it probably rained on some of the tributaries, possibly hundreds or sometimes even thousands ofkilometers away.
XAOS INSTRUCTIONS
XaoS Instructions. First, Download the correct version of the program for your computer. Installation (PC): Unzip the folder “XaoS” onto the desktop. Within this folder, there is a directory “bin”. Use the “XaoS” icon inside to run the program. Macintosh: Save “XaoS-3.2.2-MacOSX.dmg to the desktop and click on it to install.Run
FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
ONLINE FRACTAL COURSE Online Fractal Course. We are proud to announce the launching of an online fractal course. It has been developed by the Fractal Foundation in collaboration with UNM under a grant from the NM Public Education Department. While the course is primarily aimed at high school students, anyone may browse the material and do the exercises andactivities.
LEARN TO CODE!
Learn to Code! Creating fractal software is a fun and easy introduction to coding. Because fractals are made by repeating simple processes, it is actually quite easy to create simple programs that make dazzling fractal patterns. Julia and Maya – 2 interns at theFRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. FRACTAL FOUNDATION FRACTIVITIES Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, all rights reserved Fractal Foundation Fractivities FRACTAL FOUNDATION ONLINE COURSE The range from C = 0 to -.75 is the period 1 area of the bifurcation map, and is also the main body of the Mandelbrot Set. The period 2 section of the bifurcation map corresponds to the main bulb (the 'head') of the Mandelbrot Set. Each additional bifurcation in the Map corresponds to the next bulb on top of the head moving leftward on theX-axis.
FRACTAL FOUNDATION
Name: Fractal Triangles 1. Write one sentence that describes what a fractal is. 2. What are fouP types of fractal patterns that youlearned about?
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below.FRACTAL FOUNDATION
The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
WHAT ARE FRACTALS?
What are Fractals? A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are imagesof
ONLINE FRACTAL COURSE Online Fractal Course. We are proud to announce the launching of an online fractal course. It has been developed by the Fractal Foundation in collaboration with UNM under a grant from the NM Public Education Department. While the course is primarily aimed at high school students, anyone may browse the material and do the exercises andactivities.
LEARN TO CODE!
Learn to Code! Creating fractal software is a fun and easy introduction to coding. Because fractals are made by repeating simple processes, it is actually quite easy to create simple programs that make dazzling fractal patterns. Julia and Maya – 2 interns at theFRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION STORE Buy the finest fractal merchandise and apparel including shirts and hoodies with beautiful, high resolution, psychedelic designs, and support the Fractal Foundation’s educational mission. FRACTAL FOUNDATION FRACTIVITIES Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, all rights reserved Fractal Foundation Fractivities FRACTAL FOUNDATION ONLINE COURSE The range from C = 0 to -.75 is the period 1 area of the bifurcation map, and is also the main body of the Mandelbrot Set. The period 2 section of the bifurcation map corresponds to the main bulb (the 'head') of the Mandelbrot Set. Each additional bifurcation in the Map corresponds to the next bulb on top of the head moving leftward on theX-axis.
FRACTAL FOUNDATION
Name: Fractal Triangles 1. Write one sentence that describes what a fractal is. 2. What are fouP types of fractal patterns that youlearned about?
PASCAL’S SIERPINSKI TRIANGLE Pascal’s Triangle is a simple to make pattern that involves filling in the cells of a triangle by adding two numbers and putting the answer in the cell below.FRACTAL SOFTWARE
Free! FRAX (99 cents) This is an app for iPhones and iPads, and it is the best touch screen fractal explorer EVER made. It’s simply wonderful! You can pinch to zoom or spin and steer by tilting. Incredible fun, and so beautiful. FRAX Lite – a taste of FRAX. A taste of FRAX for free! Fractal to Desktop.FRACTIVITIES
Fractivities. Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I. Pierce Foundation, our fractivities are FRACTAL FOUNDATION ONLINE COURSE Although fractals are very complex shapes, they are formed by repeating a simple process over and over. Play with the fractal below by dragging the dots. We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightningbolts, blood
XAOS – FRACTAL FOUNDATION Use free software to explore fractals and create beautiful art. XaoS (https://fractalfoundation.org/resources/fractal-software/) is free software that allows us to FRACTAL FOUNDATION ONLINE COURSE The majority of a lightning bolt is generally hidden in a cloud, much as an iceberg hides beneath the ocean. Lightning can be very large, spanning several kilometers, but it is formed in microseconds. Thunder is a fractal sound. It is caused by the superheating of air. Because the pathway of the lightning bolt is a jagged fractal in 3D space FRACTAL FOUNDATION ONLINE COURSE Questions: Start with 100 fish in a pond (P 0).Assume a fertility factor of .5, and that the carrying capacity of the pond is 200. Use the Verhulst equation to calculate the number of fish at the next generation, P 1: Calculate the number at the second generation, P 2: Hint: your answer should be larger than the carrying capacity, which is unsustainable. MASKS – FRACTAL FOUNDATION Choosing a selection results in a full page refresh. Press the space key then arrow keys to make a selection. Opens in a new window. Opensexternal website.
FRACTAL FOUNDATION ONLINE COURSE The answer is that the network of tributaries collects water from a huge surface area of land and funnels it into the river. Even though it may not have rained recently where you happen to be watching the river, somewhere upstream it probably rained on some of the tributaries, possibly hundreds or sometimes even thousands ofkilometers away.
FRACTAL FOUNDATION ONLINE COURSE Now we will explore the formation of spirals in more detail, and discover some more interesting and useful facts about Fibonacci Numbers. We will be examining the concept of periodicity, which we'll also learn about in the Mandelbrot Set, but which is also important in a large number of natural systems.. Perhaps the simplest, most elegant example of a spiral in nature is a seashell. FRACTAL FOUNDATION ONLINE COURSE The Golden Ratio. The Fibonacci Sequence appears in many seemingly unrelated areas. In this section we'll see how the Fibonacci Sequence generates the Golden Ratio, a relationship so special it has even been called "the Divine Proportion."* __
Fractal Foundation
Fractals are SMART: Science, Math and Art!* About Us
* Board of Directors * Sponsors and Supporters* Please Donate
* Volunteer
* Contact Us
* Jonathan Wolfe
* Julie Tyrrell
* Fractal Shows
* First Friday Fractals* Fractals Rock!
* Fulldome Shows
* Education and Outreach * Educators’ Guide * Keynote Speaker – Dr. Jonathan Wolfe* Explore Fractals
* Fractal Software
* XaoS Instructions
* STEAM ECHO for Teachers* Fractivities
* Bingo
* Exponents
* Fibonacci Sequence and Spirals* Fractal Triangle
* Koch Curve and Coastlines* Nature Walk Bingo
* Pascal’s Sierpinski Triangle* XaoS
* Fractal Cutout Card* Fractal Trees
* Watersheds and Rivers * Fractal Tetrahedrons* Fraction Tree
* Fractal Scavenger Hunt* Flower of Life
* 3D Paper Tetrahedrons* Menger cubes
* Tic Frac Toe
* Fractal Patterns In Turbulence * Online Fractal Course* Fractal Challenge
* Learn to Code!
* Code the Rainbow Tunnel* Rainbow Tunnel 2
* Fractal Trianglethon * What are Fractals? * What is Chaos Theory?* Bookshelf
* Fractal Balloons
* Videos
* Donate
* Store
* Stay in Touch
*
* About Us
* Board of Directors * Sponsors and Supporters* Please Donate
* Volunteer
* Contact Us
* Jonathan Wolfe
* Julie Tyrrell
* Fractal Shows
* First Friday Fractals* Fractals Rock!
* Fulldome Shows
* Education and Outreach * Educators’ Guide * Keynote Speaker – Dr. Jonathan Wolfe* Explore Fractals
* Fractal Software
* XaoS Instructions
* STEAM ECHO for Teachers* Fractivities
* Bingo
* Exponents
* Fibonacci Sequence and Spirals* Fractal Triangle
* Koch Curve and Coastlines* Nature Walk Bingo
* Pascal’s Sierpinski Triangle* XaoS
* Fractal Cutout Card* Fractal Trees
* Watersheds and Rivers * Fractal Tetrahedrons* Fraction Tree
* Fractal Scavenger Hunt* Flower of Life
* 3D Paper Tetrahedrons* Menger cubes
* Tic Frac Toe
* Fractal Patterns In Turbulence * Online Fractal Course* Fractal Challenge
* Learn to Code!
* Code the Rainbow Tunnel* Rainbow Tunnel 2
* Fractal Trianglethon * What are Fractals? * What is Chaos Theory?* Bookshelf
* Fractal Balloons
* Videos
* Donate
* Store
* Stay in Touch
Fractal Foundation
* About Us
* Board of Directors * Sponsors and Supporters* Please Donate
* Volunteer
* Contact Us
* Jonathan Wolfe
* Julie Tyrrell
* Fractal Shows
* First Friday Fractals* Fractals Rock!
* Fulldome Shows
* Education and Outreach * Educators’ Guide * Keynote Speaker – Dr. Jonathan Wolfe* Explore Fractals
* Fractal Software
* XaoS Instructions
* STEAM ECHO for Teachers* Fractivities
* Bingo
* Exponents
* Fibonacci Sequence and Spirals* Fractal Triangle
* Koch Curve and Coastlines* Nature Walk Bingo
* Pascal’s Sierpinski Triangle* XaoS
* Fractal Cutout Card* Fractal Trees
* Watersheds and Rivers * Fractal Tetrahedrons* Fraction Tree
* Fractal Scavenger Hunt* Flower of Life
* 3D Paper Tetrahedrons* Menger cubes
* Tic Frac Toe
* Fractal Patterns In Turbulence * Online Fractal Course* Fractal Challenge
* Learn to Code!
* Code the Rainbow Tunnel* Rainbow Tunnel 2
* Fractal Trianglethon * What are Fractals? * What is Chaos Theory?* Bookshelf
* Fractal Balloons
* Videos
* Donate
* Store
* Stay in Touch
FLYING FRACTALS
We are making Albuquerque the Fractal Capital of the World, home of the Fractal Balloons - inspiring symbols of the beauty of math andscience!
See more
FRACTAL SHOW TICKETS First Friday Fractal shows are unfortunately halted until furthernotice
Buy Tickets
FREE FRACTAL SOFTWARE Become a fractal artist and explore fractals yourselfDownload Now
HANDS-ON FRACTIVITIES Fun, hands-on activities combining math, science and artCheck it out!
HIRE THE FRACTAL FOUNDATION Bring our awe-inspiring outreach to your school or eventWhat we do
NM SCIENCE FIESTA FRACTAL DEMOSeptember 26, 2020
Written by FRACTALMAN Jonathan Wolfe, Fractal Foundation Director demonstrates how to use the free, open-source XaoS program to create stunning algebraic fractals. Thank you to Explora and the New Mexico Science Fiesta for inviting us to participate!Uncategorized
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STEAM ECHO FOR ELEMENTARY TEACHERSSeptember 10, 2020
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FRACTALMAN
We’re excited to announce the STEAM ECHO professional development series, an innovative and collaborative professional development program for elementary and middle school teachers who want to: Learn and share best practices to engage students in Science, Technology, Engineering, Arts and Math Develop fluency delivering lessons grounded in the Next Generation Science Standards Gain tools, strategies, andUncategorized
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FRACTAL FACE MASKS ARE HERE!April 22, 2020
Written by FRACTALMAN Well pretty much everything we do at the Fractal Foundation has been paused for the moment (teaching, planetarium shows, fractal ballooning) but we’ve found a way to keep sharing fractals with the world while helping with the coronavirus crisis. Now you can stay safe in public, protect those around you, support science and matheducation
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FRACTAL CHALLENGE WINNERS IN THE NEWS...February 11, 2020
Written by FRACTALMAN We’re so proud of all the winners of the Albuquerque Fractal Challenge, and excited to see the great work these kids are doing featured on TV. Thank you to KRQE, the City of Albuquerque’s UETF, Starfield Collective, and Electric Playhouse for making this program so successful! Albuquerque works to become fractal capital of theworld
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ALBUQUERQUE FRACTAL CHALLENGE WINNERS...January 31, 2020
Written by FRACTALMAN We are so excited to announce the newest winners of the Albuquerque Fractal Challenge! We’ve selected the 8 most interesting and beautiful fractals created by students, and they are some of the best we’ve ever seen. We’ve already begun enlarging some of the winning artworks and displaying them on the sides of buildings in Albuquerque, and there’s lotsUncategorized
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FRACTALS AT MEOW WOLFNovember 7, 2019
Written
by FRACTALMAN
We are very excited to have been invited to do a free fractal workshop at Meow Wolf in Santa Fe on November 30, from 1-6 PM. The public is invited to join us for several brief video explorations of fractals starting on the hour, followed by interactive hands-on fractal making activities (“Fractivities”!). We will be teachingUncategorized
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FRACTAL CLOTHING IS HERE!September 28, 2019
Written by FRACTALMAN Click here to visit the Fractal Store Wearing fractals is FUN!!! And by purchasing fractal merchandise, you are supporting science, math and art education in New Mexico.Uncategorized
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FRACTAL BALLOONS
September 27, 2019
Written by FRACTALMAN The Fractal Foundation is incredibly excited to share not one, but TWO digitally printed fractal art balloons with the world. These are the first balloons ever of their kind, fully digitally printed mathematical artworks. Fractals are infinitely complex patterns that can be zoomed into forever. The images on the balloons are tinydetails of the
Balloons , video
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WELCOME FIBONACCI!
July 3, 2019
Written by
FRACTALMAN
The Fractal Foundation is thrilled to welcome the newest flying fractal to the fleet! Our latest infinitely complex inspiring creation “Fibonacci” was manufactured by Kubicek Balloons, and is the largest, highest resolution fractal ever printed. This art balloon contains over 340 BILLION pixels! Infinite Gratitude to Jason Fischer for generously making this fractal dream come toBalloons ,
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FRACTAL FOUNDATION IN THE NEWS!September 3, 2018
Written by JENNIFER SCHUETZ HADLEY We enjoyed being interviewed by the KRQE Morning Show on Friday, August 31, 2018, discussing what fractals are, what we do and what we’re working on next. Check it out here!Uncategorized
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Fractals are SMART: Science, Math & Art!Details
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