Seeing Wang Qi improving the Fla Cloud Map, Zhen Chan was very excited.
In his view, Wang Qi had finally brought forward so results that he himself could understand. If ancient cultivators from tens of thousands of years ago could draw such diagrams, he could definitely understand them too! Didn't modern cultivators always say that the Immortal Dao was continuously developing?
However, when Zhen Chan asked Wang Qi to explain the underlying principles, Wang Qi rolled his eyes and said, "History is progressing, but only within the two thousand years since the establishnt of the modern thods and the period when the ancient thod erged from nothing. Old man, don't forget, your era belonged to that prolonged regression, the very bottom of that decline."
Zhen Chan beca angry and embarrassed, "You figure it out yourself then, I'll just watch."
The top student scratched his head and asked, "Old man, do you know about a great cultivator from the sa era as the Geotric Demon Lord, who is now called the Geotric God, Oulide?"
"Of course, I know; 'Sky Drawing Five Techniques' and 'Sky Drawing Five Queries' were also extrely famous divine skills in ancient tis."
Wang Qi then asked, "Do you know the mathematical reasoning behind the Geotric God's Sky Drawing Five Techniques?"
"Uh..."
"Then there's nothing to discuss." Wang Qi spread his hands, "Sky Drawing Five Theories, Sky Drawing Five Certainties, Twenty-Three anings are the very basics. If even Euler's correct universe isn't sothing you have unraveled, you shouldn't even think about stepping into this field."
Sky Drawing Five Theories and Sky Drawing Five Queries are what are called on Earth as Euclid's five postulates and five common notions. Surface Geotry, Hilbert's High-dinsional Phase Space, Fractals, and Fractional Dinsions are all based on Euclidean Geotry.
Fractional Dinsions, as it is, refer to fractional dinsions. All fractals can be described with fractional dinsions.
Zhen Chan was relentless. Wang Qi sighed and said, "Watch if you like, just don't regret it."
Afterwards, the top student ceased regarding Zhen Chan and began to think on his own.
"This has an area, undoubtedly it is two-dinsional," he mused, biting his pen, "According to the definition where the fractal dinsion is greater than the topological dinsion, this diagram should be greater than two dinsions but less than three."
While thinking, Wang Qi wrote on the paper, "Greater than two 'Phases' less than three 'Phases'."
"'Phase' is the term used by Shenzhou Immortal Dao to interpret 'dinsion.'"
This had beco his recent habit, insisting on using Shenzhou's mathematical language when drafting.
After writing this sentence, Zhen Chan felt like he was going crazy. Having attended many classes at the Immortal Institute with Wang Qi, he could understand what "two phases" and "three phases" were. But "greater than two phases less than three phases"? What the heck is that!
Since Wang Qi had already warned him, the old man felt too embarrassed to ask again due to his pride.
Next, Wang Qi wrote down this formula in Shenzhou's language: K=(1/L)－Df.
"If a figure is composed of b smaller figures similar to the original figure, each reduced by a factor of 1/a, we have: a^D=b, D=(lnb)/(lna)… Roughly partition this figure… like this, then partition again…"
Wang Qi continuously calculated, calculating the fractal dinsion, the expression of the fractal, everything about the fractal!
The Jade Ring "Mathematics" emitted a faint glow. Although it fell short in logarithms, its reasonable use could still reduce so of Wang Qi's workload.
Wang Qi kept calculating, all the way until dawn.
When Wang Qi stretched and wrote down the last formula, he realized he might have gotten a bit too absorbed in his calculations, "Crap, calculated too much… Damn, I really want to sleep!"
Zhen Chan sighed, "You clearly already extracted the useful part from the entire mory Map…"
The young man waved his hand, "That's still not enough. The Spirit Treasure Fractal Map is a fractal, not sothing that can be accurately depicted just by intuition; in fact, the Fla Cloud Map only provides a rough image."
"What about the complete one?"
Wang Qi triumphantly pointed at the formula on the paper, "This is it! When a pen can't accurately depict a shape, we must use mathematics to portray it."
Zhen Chan stared at Wang Qi's formula for a long ti. Finally, the old man let out a sigh of frustration, "I... don't understand!"
"So, there's no need to fear using up spirit! Even an incomplete Spirit Treasure Fractal Map has helped stabilize my Heart Demon and nurture my spirit, so it's unreasonable that a complete version wouldn't instantly recover my spirit as well!"
The elderly man hesitated, "This... Cultivation matters should not be taken lightly. This thod you have just created—it's best not to try it at a critical mont like this."
"I'm practicing scientific Cultivation guided by theory!" Wang Qi, undeterred, crossed his legs and began to close his eyes in reflection.
The first step in reflection was sketching a mory Map in his mind. For Wang Qi, who had already mastered the expression of the Upper Pure Fractal Diagram, this step was far simpler than sketching the Fla Cloud Map.
Soon, a complex figure appeared in Wang Qi's mind. That feeling of grasping everything about oneself erged again!
No, this ti it wasn't just a feeling of grasping. The young man felt his "self" and "Spirit Treasure" transform into a vortex, starting to madly devour mories and the "Id" and "Primitive Self"!
"This is..."
Then, the "self" began to grow stronger, and Wang Qi felt his Soul Power increasing wildly!
Changes in the soul triggered changes in mana. Wang Qi's mana began to gradually rge into his soul.
At that mont, a strand of refined mana extended from Wang Qi's Dantian. This strand of mana, concentrated yet unreleased, directly followed Wang Qi's soul and stabbed into the vortex created by the Spirit Treasure Fractal Diagram.
"The Book of Geotry? Is this the Heavenly Position Magic Axis?"
Wang Qi was stunned. It was within his expectations that the Spirit Treasure Fractal Diagram could assist in cultivating the soul. However, the fact that the diagram induced changes in his own mana was unexpected.
Realizing sothing was amiss, Wang Qi prepared to cease his Cultivation. However, as soon as the Heavenly Position Magic Axis representing the number axis delved deeper into the fractal vortex, Wang Qi felt his mana and soul start to spin wildly, completely out of control!
The chaos in the soul bred illusions.
One by one, the scenes before Wang Qi's eyes faded, leaving only nurous complex and splendid visions. Tortuous coastlines, rugged mountain ranges, rough fault planes, everchanging clouds, winding rivers, crisscrossing blood vessels, and a dazzling sky full of stars...
Gradually, these scenes were abstracted into geotric figures by the power of the Book of Geotry. All these figures were highly irregular and rough.
These were fractals, geotric objects of complex irregularity that traditional Euclidean geotry cannot describe!
The fractals continued to be simplified. Irregular, fragnted, fractional... Concepts like these flooded Wang Qi's will.
Then, the young man felt the Heavenly Position Magic Axis connected to the Spirit Treasure Fractal Diagram start to converge.
Fractals, being fractal dinsions, naturally had converging number axes.
The scholar felt a bone-chilling coldness. The initial theory of the Book of Geotry was based on Euclidean geotry. Only by integrating it with the Yao Ding Calculating Scripture to form the Heavenly Position Technique could one delve into higher levels of geotry. But a converging number axis... could not be compatible with traditional Euclidean geotry!
As soon as the number axis began to converge, Wang Qi felt a sharp pain emanating from his Dantian. Then, his entire body's Cultivation shattered and clashed. With his mana surging violently, Wang Qi couldn't help but spit out a mouthful of blood.
Mao Zimiao, dumbstruck, watched this unfold. She had been awakened by the abnormal fluctuations of mana in the room and had just witnessed the scene. The imnse shock left her stunned for a few seconds. Then, the girl cried out in a piercing voice, "Xiao Qi!"
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