Building a new computer for generating fractals

I've recently been getting into graphic design using programs like Adobe Illustrator, JWildFire, and Mandelbulb3D to create fractal images.
Currently, I have:
-8 core AMD FX-8320
-8GB DDR3 1600 RAM
-MSI GTX 660 twin frozr
Fractal images are made by running certain equations millions of times and outputting a map of it, and I've notice that when rendering these the graphics card is hardly ever stressed/used, the RAM is around 40% use, and the CPU at 90%+. And it takes hours to render an image.

I'm wondering if would really be worth upgrading? Would the performance increase be worth building a new system with Intel Six core or AMD 9590?
Also, I was wondering what main things would improve computing power/speed...(# of cores, DDR3 vs DDR4, motherboard chipset)

Thanks in advance for any advice.

What budget what country?

Also why not use GPU accelerated software like this one? Fractron9000

[GPU Computing] Fractron 9000: GPU (OpenCL) Fractal Flame Renderer

Name must be from the 2000s

or there's this one some guy made, both of these list openCL, so you'd probably want an AMD card
http://www.fractalforums.com/announcements-and-news/fractorium-a-new-gpu-accelerated-flam3-fractal-flame-renderer/

but try those with your 660, should be faster than just the CPU anyways

or there's this one with marketing hype rather than being FOSS, dunno if it's FOSS though, probably not given the pricing, but I guess it might end up being better due to cost? no clue but the video on the page looks neat

Chaotica Studio 1.0 Licence €89
Chaotica Studio licence for all 1.x versions, no resolution or animation limits.

Chaotica HD 1.0 Licence €25.00
Chaotica HD licence for all 1.x versions, 4mpix (e.g. 2560x1600) resolution limit and 3 minute 720p animation limit.

http://chaoticafractals.com/

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9590 is never worth buying for anything but heatsink stress testing.

Wow, thanks man, I appreciate the advice. Especially the money saving advice. I will definitely give those programs a try
My budget would be around $700, and I'm in the US.

Seems basic X99 stuff is basically your limit from the get go

so ya maybe find a GPU accelerated one you like, see if it needs CUDA or OpenCL, then upgrade your GPU, maybe upgrade the CPU later

PCPartPicker part list: http://pcpartpicker.com/p/tWZxmG
Price breakdown by merchant: http://pcpartpicker.com/p/tWZxmG/by_merchant/

CPU: Intel Core i7-5820K 3.3GHz 6-Core Processor ($376.99 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.74 @ Amazon)
Motherboard: Asus X99-A/USB 3.1 ATX LGA2011-3 Motherboard ($249.00 @ Amazon)
Memory: Crucial 16GB (2 x 8GB) DDR4-2133 Memory ($64.99 @ Adorama)
Total: $720.72
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-03-04 23:21 EST-0500

Awesome, you answered that a lot faster and with a ton more information that I could have ever expected.
Those are pretty similar to the parts I had in mind, I always get stuck on the motherboard
Thanks again for the help and a positive first time on the forum!

I agree with @Streetguru
X99 would be a very good platform for you to jump on.
And with the parts he selected you should be good to go.
Maybe grab a 4x4GB kit instead of 2x8GB to utilize quadchannel on X99.
This could improve rendering abit.
In terms of pricing 2x8GB or 4x4GB kit should be pretty much similar.

What software were you using before?

I use Mandelbulb3D and JWildFire for the most part. I haven't really been able to find something similar to Mandelbulb3D with actual 3D fractals that you can explore and zoom up to 1x10^13.

Seems like it supports open CL, were you already doing that?
http://libregraphicsworld.org/blog/entry/mandelbulber-1.09-starts-rendering-3d-fractals-on-gpu