The content now includes over 2000 pages of pdf content for the entire SL and HL Analysis syllabus and also the SL Applications syllabus. This has been designed specifically for teachers of mathematics at international schools. If you are a teacher then please also visit my new site. You can modify the code to run this here. We can explore what happens when we change the iterations very slightly. You might want to explore the idea of fractals in delving into this topic in more detail. You could zoom into a detailed picture and see the same patterns repeating. This fern is an example of a self-similar pattern – i.e one which will look the same at different scales. It’s quite amazing to think that a simple computer program can create what looks like art – or indeed that is can replicate what we see in nature so well. Transformations 2 and 3 fill in the bottom left and right leaflet (respectively) and transformation 4 fills in the stem. Transformation 1 is most likely and therefore this fills in the smaller leaflets. If we want to understand what is happening here we can think of each transformation as responsible for a different part of our fern. The graph above was generated with 40,000 iterations – let’s see how it develops over time: I mark this on my graph and carry on again.
I then repeat this process – say this time I generate the number 90. Say I generate the number 36 – therefore I will apply transformation 1.Īnd my new coordinate is (0,1.6).
#Dragon curve ultra fractal generator#
I can run a generator from 1-100 and assign 1-85 for transformation 1, 86-92 to transformation 2, 93-99 for transformation 3 and 100 for transformation 4. So, I start with (0,0) and then use a random number generator to decide which transformation to use. Transformation 4: (0.01 probability of occurrence)
Transformation 3: (0.07 probability of occurrence) Transformation 2: (0.07 probability of occurrence) Transformation 1: (0.85 probability of occurrence) What we are seeing is the result of 40,000 individual points – each plotted according to a simple algorithm. I downloaded the Python code from the excellent Tutorialspoint and then modified it slightly to run on. This pattern of a fern pictured above was generated by a simple iterative program designed by mathematician Michael Barnsely. If you are a teacher then please also visit my new site: for over 2000+ pdf pages of resources for teaching IB maths!
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