Using Two "Weird" Apps to Visualize Baffling Mathematical Concepts

Innovative design of educational technology can help learners literally grasp the sophisticated concepts with their own hands

Title photo



Charles Ai

Updated 2018-10-09

Mysteries of Fractal

Mysteries of Fractal, Logo & Landing Page

Ah, fractals. Those never-ending geometric patterns where each piece resembles the whole. Mysteries of Fractal makes this heady concept a lot easier to understand. This three-chapter course goes deep on the formula behind fractals, and even builds one of these beautifies for you based on a few inputs. Or just skip the course and play, creating your own fractals or zooming in on a few ready-made examples.

Mysteries of Fractal, Interface

The intricately designed UI with the dark background and bold colours creates an entirely appealing and immersive experience for its users

Mysteries of Fractal, "Create" Module

By modifying only two parameters, we can draw countless intriguing graphics, or even shoot a short video like the above

Whether you are a math fanatic or art lover, this app can bring you a rare opportunity to marvel at the enigmatic yet spectacular interaction between the two seemingly remotely related disciplines. Within the app, the overwhelmingly simplified, and perhaps quite abstract and tedious, math formula was as if enchanted with the magical power to be able to evoke our most delicate feelings that reflect aesthetic sensibilities out from nowhere. Thanks to robust graphics computing power of iPad and iPhone, users can witness the real-time generated, dynamic fractal images, with magnification up to 20,000 times, right on their screen.

Mysteries of Fractal, Personal Drawings 1 & 2

Mysteries of Fractal, Personal Drawings 3 & 4

Some of my "drawings" produced in the "create" module of the app. It's so addictive, I must admit!

The instructions in the short course are also quite patient and inviting, adding more educational values to its possible classroom integration. One of its suitable appearances can be after the learning of complex numbers as a relaxing wrap-up of the concepts to help students better digest the somehow tricky properties of complex numbers.

The Fourth Dimension

The Fourth Dimension, Logo and Landing Page

Warning: Trying to warp your head around this unapologetically abstruse app can be tough. But physics and maths geeks will appreciate this playful, funny 30-page interactive book. Explore the fourth dimension concepts by manipulating a tesseract (the 4D equivalent of a cube) and watching its shadow projected onto a 3D grid. The spacey sound effects are a bonus.

The Fourth Dimension, 3D or 4D?!

Is it 3D or 4D after all?

As pitiful creatures confined in three-dimensional space, we would deem any glimpse of the higher dimension as an awe-inspiring, one-of-a-life-time experience. While a direct demonstration of any 4D objects in our 3D world is entirely out of the question, this app employs a unique 3D touch interface that can help the users have a close look at how objects in the 4th dimension can leave perceivable traces in our 3D world.

The Fourth Dimension, Explanation of Interaction between Higher and Lower Dimensions

The analogy used to shed light on  the properties of the projection from a higher dimension to a lower one

The Fourth Dimension, the Divine Illumination (imaginary light from 4D)

Religious people might be very excited to witness this Divine Illumination

With rather tempting and a bit funny instructions, the app gently guides us to understand the seemingly impenetrable 4D world by drawing analogies between the lower dimensions and higher ones. Through interactive demonstrations, it patiently helps us build confidence in those commons facts before letting us embark on the real mind-blowing exploration. Even when we finally meet the mystifying tesseract per se, the app would juxtapose the 3D model and the 4D projection and pose review questions on us to encourage the users to interpret what we have seen before rushing to the theoretical explanations — a prerequisite of a successful course.


Both apps function as interactive ebooks, with clearly separated chapters and sections, and abundant hands-on activities to engage users in their learning experience. They both succeed in creating an emotional bond between the target knowledge and its learners themselves by using striking animations and graphics models to itch their curiosity from the very first page to the end. For math classes, where students are prone to lose focus and confidence on what they are supposed to learn, using most visually accessible approaches to appeal students and have them emotionally committed to their learning is much more beneficial than traditional methods. 

If we compare the structure of the two apps, Mysteries of Fractal is arguably a more well-rounded educational app in that its "creator" module can be an ideal source for students and teachers to stir their imagination and creativity even when they find complex numbers are too intimidating — a wonderful mitigation of students' stress and cultivation of their interests in applied mathematics!

Thank you very much for your reading! Feel free to leave a comment below or send me a message of feedback from here. You can also find the links of my social network at the bottom of the page.


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